Topic Editors

1. Faculty of Mechanical Engineering, São Paulo State University, Bauru 17033-360, São Paulo, Brazil
2. Department of Electrical Engineering, Federal University of Technology—Parana, Ponta Grossa 84017-220, Paraná, Brazil
Department of Mathematics, Federal University of Technology – Paraná (UTFPR), Ponta Grossa 84016-210, PR, Brazil
Dr. Átila Madureira Bueno
Control and Automation Engineering Department, Institute of Science and Engineering, São Paulo State University (UNESP), Sorocaba, SP, Brazil
Automation and Control Laboratory (LAC), Telecom and Control Department, Polytechnique School, University of São Paulo, São Paulo 05508-010, SP, Brazil
Dr. Marcus Varanis
Physics Institute, Federal University of Mato Grosso do Sul (UFMS), 79070-900 Campo Grande, Brazil

Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems

Abstract submission deadline
31 October 2024
Manuscript submission deadline
31 December 2024
Viewed by
30539

Topic Information

Dear Colleagues,

The need for dynamics and the control of nonlinear oscillating systems is ubiquitous in engineering, since real-world engineering systems are, in general, nonlinear and oscillatory.

This multidisciplinary field encompasses computation, physics, mathematics, electrical and mechanical engineering, chemical processes, etc.

The objective of this theme is to propose a set of publications that will provide a forum for discussing and disseminating the latest approaches, methodologies, results, and current challenges in nonlinear dynamics and chaotic systems.

Contributions can include all analytical, computational, and experimental aspects of nonlinear dynamics, chaos and control including fractional approaches, electromechanical systems at MACRO, MEMS, and NEMS scales, nonideal oscillating systems (limited power supplies) and novel phenomena and behaviors regarding several aspects of symmetry in nonlinear dynamics, chaos and control.

This theme will also provide a great opportunity for disseminating recent developments in analytical and numerical techniques, and discussing novel phenomena and behaviors regarding several aspects of nonlinear dynamics and control. In addition, works related to relevant and current issues, such as epidemiological models, rumor dissemination and complex systems, are also welcome.

Finally, researchers and practitioners are invited to submit their original research work on the rapidly developing field of nonlinear dynamics and control of system oscillations and their applications to engineering and science. Therefore, we encourage the submission of the practitioners’ latest unpublished works.

Prof. Dr. José Balthazar
Prof. Dr. Angelo Marcelo Tusset
Dr. Átila Madureira Bueno
Dr. Diego Colón
Dr. Marcus Varanis
Topic Editors

Keywords

  • nonlinear dynamics, chaos in oscillating systems at macro-, micro- or nano-scales; systems in fractional orders; entropy; fuzzy systems; complex systems
  • global nonlinear dynamics for engineering design and system safety: erosion of basins of attraction—dynamical integrity
  • MEMs systems; atomic force microscopy
  • nonlinear control of nonlinear oscillating systems at macro-, micro- or nano-scales; optimal, robust and adaptive control of nonlinear oscillating systems; process control of nonlinear oscillating systems in engineering processes; metamaterials and their control
  • sensitivity analysis in macro and MEMS modeling; polynomial chaos
  • energy transfer between oscillators; synchronization
  • biomathematics; bio-inspired models
  • rumor and information dissemination
  • acoustic levitation
  • astrodynamics

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Applied Sciences
applsci
2.7 5.3 2011 16.9 Days CHF 2400 Submit
Axioms
axioms
2.0 - 2012 21.8 Days CHF 2400 Submit
Entropy
entropy
2.7 4.9 1999 20.8 Days CHF 2600 Submit
Mathematics
mathematics
2.4 4.0 2013 16.9 Days CHF 2600 Submit
Symmetry
symmetry
2.7 5.4 2009 16.2 Days CHF 2400 Submit
Dynamics
dynamics
- 1.2 2021 12.7 Days CHF 1000 Submit
Machines
machines
2.6 3.0 2013 15.6 Days CHF 2400 Submit

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Published Papers (30 papers)

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12 pages, 3939 KiB  
Article
Young’s Modulus and Hardness Identification of Extruded Aluminum by Scratching Damper
by Chun-Nam Wong, Anand Vyas, Wai-On Wong and Ruqi Sun
Machines 2024, 12(6), 413; https://doi.org/10.3390/machines12060413 (registering DOI) - 17 Jun 2024
Abstract
A special vibration damper is proposed for Young’s modulus and hardness identification through a scratching process on extruded aluminum. This paper presents the design and working principle of a scratching damper based on a scratching device. A non-contact electromagnetic shaker is used to [...] Read more.
A special vibration damper is proposed for Young’s modulus and hardness identification through a scratching process on extruded aluminum. This paper presents the design and working principle of a scratching damper based on a scratching device. A non-contact electromagnetic shaker is used to generate the shaking force for test sample vibration. The required forces on the scratched material during the scratching process are generated by an adjustable compression spring. The proposed damper is designed and tested on an extruded aluminum 3004 sample for the determination of its Young’s modulus and hardness, and validation is performed using the standard test instruments. The physical dimensions of the scratching tracks are measured using a microscope and utilized to compute the scratching energy factor. Load curves are obtained at different divisions of the scratching process. The loop energy during the scratching process of the tested object is measured and used for the determination of sample material properties. Furthermore, the energy conservation law, scratch energy release rate of semi-conical scratch head, and loop energy release rate are established to determine the Young’s modulus and hardness of the sample. Their estimation accuracies are evaluated. The proposed method has several advantages over the traditional methods, including low cost, directness, and high repeatability. The results suggest this to be used as an alternative to the standard modulus and hardness tester. Full article
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24 pages, 4837 KiB  
Article
A Comparative Study of Different CFD Codes for Fluidized Beds
by Parindra Kusriantoko, Per Fredrik Daun and Kristian Etienne Einarsrud
Dynamics 2024, 4(2), 475-498; https://doi.org/10.3390/dynamics4020025 (registering DOI) - 16 Jun 2024
Viewed by 105
Abstract
Fluidized beds are pivotal in the process industry and chemical engineering, with Computational Fluid Dynamics (CFD) playing a crucial role in their design and optimization. Challenges in CFD modeling stem from the scarcity or inconsistency of experimental data for validation, along with the [...] Read more.
Fluidized beds are pivotal in the process industry and chemical engineering, with Computational Fluid Dynamics (CFD) playing a crucial role in their design and optimization. Challenges in CFD modeling stem from the scarcity or inconsistency of experimental data for validation, along with the uncertainties introduced by numerous parameters and assumptions across different CFD codes. This study navigates these complexities by comparing simulation results from the open-source MFIX and OpenFOAM, and the commercial ANSYS FLUENT, against experimental data. Utilizing a Eulerian–Eulerian framework and the kinetic theory of granular flow (KTGF), the investigation focuses on solid-phase properties through the classical drag laws of Gidaspow and Syamlal–O’Brien across varied parameters. Findings indicate that ANSYS Fluent, MFiX, and OpenFOAM can achieve reasonable agreement with experimental benchmarks, each showcasing distinct strengths and weaknesses. The study also emphasizes that both the Syamlal–O’Brien and Gidaspow drag models exhibit reasonable agreement with experimental benchmarks across the examined CFD codes, suggesting a moderated sensitivity to the choice of drag model. Moreover, analyses were also carried out for 2D and 3D simulations, revealing that the dimensional approach impacts the predictive accuracy to a certain extent, with both models adapting well to the complexities of each simulation environment. The study highlights the significant influence of restitution coefficients on bed expansion due to their effect on particle–particle collisions, with a value of 0.9 deemed optimal for balancing simulation accuracy and computational efficiency. Conversely, the specularity coefficient, impacting particle–wall interactions, exhibits a more subtle effect on bed dynamics. This finding emphasizes the critical role of carefully choosing these coefficients to effectively simulate the nuanced behaviors of fluidized beds. Full article
17 pages, 8160 KiB  
Article
PMT Fluorescence Signal Denoising Processing Based on Wavelet Transform and BP Neural Network
by Jiehui Liu, Yunhan Zhang, Jianshen Li, Yadong Zhao, Jinxi Guo, Lijie Yang and Haichao Zhao
Appl. Sci. 2024, 14(11), 4866; https://doi.org/10.3390/app14114866 - 4 Jun 2024
Viewed by 349
Abstract
Air is the environmental foundation for human life and production, and its composition changes are closely related to human activities. Sulfur dioxide (SO2) is one of the main atmospheric pollutants, mainly derived from the combustion of fossil fuels. But SO2 [...] Read more.
Air is the environmental foundation for human life and production, and its composition changes are closely related to human activities. Sulfur dioxide (SO2) is one of the main atmospheric pollutants, mainly derived from the combustion of fossil fuels. But SO2 is a trace gas in the atmosphere, and its concentration may be less than one part per billion (ppb). This paper is based on the principle of photoluminescence and uses a photomultiplier tube (PMT) as a photoelectric converter to develop a device for real-time detection of SO2 concentration in the atmosphere. This paper focuses on the impact of noise interference on weak electrical signals and uses wavelet transform to denoise the signals. At the same time, considering that the photoelectric system is susceptible to temperature changes, a multi parameter fitting model is constructed, and a BP neural network is used to further process the signal, separating the real data from the original data. Finally, a high-precision and wide-range trace level sulfur dioxide concentration detection device and algorithm were obtained. Full article
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13 pages, 279 KiB  
Article
Attached Flows for Reaction–Diffusion Processes Described by a Generalized Dodd–Bullough–Mikhailov Equation
by Carmen Ionescu and Iulian Petrisor
Symmetry 2024, 16(5), 531; https://doi.org/10.3390/sym16050531 - 28 Apr 2024
Viewed by 547
Abstract
This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new [...] Read more.
This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new variable called the flow and (ii) a forced decomposition of the derivative-free term so that the flow appears explicitly in it. The resulting reduced equation is solved using specific balancing rules. Only step (i) would lead to an Abel-type equation with complicated integral solutions. Completed with (ii) and with the graduation procedure, the attached flow method used in the paper, without requiring such a great effort, allows for the obtaining of accurate analytical solutions. The method is applied here to a subclass of reaction–diffusion equations, the generalized Dodd–Bulough–Mikhailov equation, which includes a translation of the variable and nonlinearities up to order five. The equation is solved for each order of nonlinearity, and the solutions are discussed following the values of the parameters involved in the equation. Full article
15 pages, 659 KiB  
Article
Auto-Correlation Functions of Chaotic Binary Sequences Obtained by Alternating Two Binary Functions
by Akio Tsuneda
Dynamics 2024, 4(2), 272-286; https://doi.org/10.3390/dynamics4020016 - 16 Apr 2024
Viewed by 392
Abstract
This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and [...] Read more.
This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and give the theoretical auto-correlation functions of the new binary sequences, which are expressed by the auto-/cross-correlation functions of the two chaotic binary sequences generated by a single binary function. Furthermore, some numerical experiments are performed to confirm the validity of the theoretical auto-correlation functions. Full article
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27 pages, 2406 KiB  
Article
Bayesian Inference of Recurrent Switching Linear Dynamical Systems with Higher-Order Dependence
by Houxiang Wang and Jiaqing Chen
Symmetry 2024, 16(4), 474; https://doi.org/10.3390/sym16040474 - 13 Apr 2024
Viewed by 536
Abstract
Many complicated dynamical events may be broken down into simpler pieces and efficiently described by a system that shifts among a variety of conditionally dynamical modes. Building on switching linear dynamical systems, we develop a new model that extends the switching linear dynamical [...] Read more.
Many complicated dynamical events may be broken down into simpler pieces and efficiently described by a system that shifts among a variety of conditionally dynamical modes. Building on switching linear dynamical systems, we develop a new model that extends the switching linear dynamical systems for better discovering these dynamical modes. In the proposed model, the linear dynamics of latent variables can be described by a higher-order vector autoregressive process, which makes it feasible to evaluate the higher-order dependency relationships in the dynamics. In addition, the transition of switching states is determined by a stick-breaking logistic regression, overcoming the limitation of a restricted geometric state duration and recovering the symmetric dependency between the switching states and the latent variables from asymmetric relationships. Furthermore, logistic regression evidence potentials can appear as conditionally Gaussian potentials by utilizing the Pólya-gamma augmentation strategy. Filtering and smoothing algorithms and Bayesian inference for parameter learning in the proposed model are presented. The utility and versatility of the proposed model are demonstrated on synthetic data and public functional magnetic resonance imaging data. Our model improves the current methods for learning the switching linear dynamical modes, which will facilitate the identification and assessment of the dynamics of complex systems. Full article
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19 pages, 6819 KiB  
Article
A New Chaos-Based Image Encryption Algorithm Based on Discrete Fourier Transform and Improved Joseph Traversal
by Mingxu Wang, Xianping Fu, Xiaopeng Yan and Lin Teng
Mathematics 2024, 12(5), 638; https://doi.org/10.3390/math12050638 - 21 Feb 2024
Cited by 1 | Viewed by 770
Abstract
To further enhance the security of image encryption, a new chaos-based image encryption algorithm (IEA) based on discrete Fourier transform and Joseph traversal is proposed to encrypt the plain image in both the frequency domain and space domain simultaneously. In the proposed IEA, [...] Read more.
To further enhance the security of image encryption, a new chaos-based image encryption algorithm (IEA) based on discrete Fourier transform and Joseph traversal is proposed to encrypt the plain image in both the frequency domain and space domain simultaneously. In the proposed IEA, the logistic map is used to generate the appropriate chaotic sequence, and the improved Joseph traversal is used to scramble the image in different starting positions and variable step sizes. Then, block diffusion is performed at the end. The main finding concerning the proposed IEA is that the combination of discrete Fourier transform and Joseph traversal can enhance the security of the image information, which has been validated by measuring the performance in resisting the common types of attacks. Full article
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20 pages, 5238 KiB  
Article
Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers
by Erman Ozpolat and Arif Gulten
Appl. Sci. 2024, 14(3), 1311; https://doi.org/10.3390/app14031311 - 5 Feb 2024
Viewed by 669
Abstract
This paper explores the synchronization and implementation of a novel hyperchaotic system using an adaptive observer. Hyperchaotic systems, known for possessing a greater number of positive Lyapunov exponents compared to chaotic systems, present unique challenges and opportunities in control and synchronization. In this [...] Read more.
This paper explores the synchronization and implementation of a novel hyperchaotic system using an adaptive observer. Hyperchaotic systems, known for possessing a greater number of positive Lyapunov exponents compared to chaotic systems, present unique challenges and opportunities in control and synchronization. In this study, we introduce a novel hyperchaotic system, thoroughly examining its dynamic properties and conducting a comprehensive phase space analysis. The proposed hyperchaotic system undergoes validation through circuit simulation to confirm its behavior. Introducing an adaptive observer synchronization technique, we successfully synchronize the dynamics of the novel hyperchaotic system with an identical counterpart. Importantly, we extend the application of this synchronization method to the domain of secure communication, showcasing its practical usage. Simulation outcomes validate the effectiveness of our methodology, demonstrating favorable results in the realm of adaptive observer-based synchronization. This research contributes significantly to the understanding and application of hyperchaotic systems, offering insights into both the theoretical aspects and practical implementation. Our findings suggest potential advancements in the field of chaotic systems, particularly in their applications within secure communication systems. By presenting motivations, methods, results, conclusions and the significance of our work in a more appealing manner, we aim to engage readers and highlight the innovative contributions of this study. Full article
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14 pages, 660 KiB  
Article
Nonlinear Medical Ultrasound Tomography: 3D Modeling of Sound Wave Propagation in Human Tissues
by Maxim Shishlenin, Andrey Kozelkov and Nikita Novikov
Mathematics 2024, 12(2), 212; https://doi.org/10.3390/math12020212 - 9 Jan 2024
Viewed by 858
Abstract
The article aimed to show the fundamental possibility of constructing a computational digital twin of the acoustic tomograph within the framework of a unified physics–mathematical model based on the Navier–Stokes equations. The authors suggested that the size of the modeling area is quite [...] Read more.
The article aimed to show the fundamental possibility of constructing a computational digital twin of the acoustic tomograph within the framework of a unified physics–mathematical model based on the Navier–Stokes equations. The authors suggested that the size of the modeling area is quite small, sound waves are waves of “small” disturbance, and given that a person consists of more than 60% water, human organs can be modeled using a liquid model, taking into account their density. During numerical experiments, we obtained the pressure registered in the receivers that are located on the side walls of the tomograph. The differences in pressure values are shown depending on the configuration of inclusions in the mannequin imitating internal organs. The results show that the developed technology can be used to probe the human body in medical acoustic tomographs and determine the acoustic parameters of the human body to detect neoplasms. Full article
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31 pages, 14917 KiB  
Article
Improved Square-Root Cubature Kalman Filtering Algorithm for Nonlinear Systems with Dual Unknown Inputs
by Zihao Lu, Na Wang and Shigui Dong
Mathematics 2024, 12(1), 99; https://doi.org/10.3390/math12010099 - 27 Dec 2023
Cited by 1 | Viewed by 682
Abstract
For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) [...] Read more.
For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms. Full article
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22 pages, 636 KiB  
Article
A Novel Dynamic S-Box Generation Scheme Based on Quantum Random Walks Controlled by a Hyper-Chaotic Map
by Lijun Zhang, Caochuan Ma, Yuxiang Zhao and Wenbo Zhao
Mathematics 2024, 12(1), 84; https://doi.org/10.3390/math12010084 - 26 Dec 2023
Cited by 2 | Viewed by 699
Abstract
For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for [...] Read more.
For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel scheme for constructing a dynamic S-Box based on the new model is proposed. Through aperiodic evaluation and statistical complexity measurement, it is shown that the compound chaotic system has features such as complex structure and stronger randomness than classical chaotic systems. Based on the chaotic sequence generated by the composite system, we design a dynamic S-Box generation mechanism. The mechanism can quickly generate high-security S-Boxes. Then, an example of randomly generating S-Boxes is given alongside an analytical evaluation of S-Box standard performance criteria such as bijection, boomerang uniformity, bit independence, nonlinearity, linear approximate probability, strict avalanche effect, differential uniformity, the and generalized majority logic criterion. The evaluation results confirm that the performance of the S-Box is excellent. Thus, the proposed dynamic S-Box construction technique can be used to generate cryptographically strong substitution-boxes in practical information security systems. Full article
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14 pages, 6570 KiB  
Article
Dynamics of Semiconductor Laser Coupled with Two External Cavities
by Salah Abdulrhmann, Abu Mohamed Alhasan and A. Y. Madkhli
Appl. Sci. 2023, 13(23), 12827; https://doi.org/10.3390/app132312827 - 29 Nov 2023
Viewed by 735
Abstract
An investigation into the dynamic states and relative intensity noise of laser diodes subjected to double optical feedback has been conducted. We employed modified and improved time-delay rate equations to account for double external optical feedback. The dynamic states and noise of lasers [...] Read more.
An investigation into the dynamic states and relative intensity noise of laser diodes subjected to double optical feedback has been conducted. We employed modified and improved time-delay rate equations to account for double external optical feedback. The dynamic states and noise of lasers will be investigated using bifurcation diagrams of the output photon number, its temporal variations, and the intensity noise of the laser. This analysis considers feedback strengths due to the double external cavity and their spacing from the front facet of the laser with and without phase due to feedback. The results reveal that considering phase causes significant variations in laser intensity and a phase shift in the temporal variations of the laser output. This results in relative intensity noise suppression and a frequency shift in the intensity noise spectrum. These findings represent new contributions to our understanding of the reliance of lasing frequency shift on the phase due to feedback, regardless of whether feedback originates from a single or double external cavity. We investigated the optimal conditions corresponding to stable dynamic states of the laser with the lowest noise level. Additionally, we identified conditions that result in chaotic dynamics, where the spectrum does not convey information about the laser system. These insights have potential applications in chaotic and secure optical data encryption. Full article
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16 pages, 1962 KiB  
Article
Adaptive Anti-Disturbance Control of Dissolved Oxygen in Circulating Water Culture Systems
by Xiaonan Yao, Gang Zhang, Song Yang and Yuehua Chen
Symmetry 2023, 15(11), 2015; https://doi.org/10.3390/sym15112015 - 2 Nov 2023
Viewed by 767
Abstract
In the three-dimensional culture model, the breeding basket of the culture area is symmetrical and it is important to control the dissolved oxygen in the symmetrical region to improve the culture efficiency. Practical engineering issues, such as the influence of flow rate, pH, [...] Read more.
In the three-dimensional culture model, the breeding basket of the culture area is symmetrical and it is important to control the dissolved oxygen in the symmetrical region to improve the culture efficiency. Practical engineering issues, such as the influence of flow rate, pH, water temperature, and biological oxygen consumption on the dissolved oxygen content in the circulating water culture system, must be considered along with the presence of modeling errors in the control model. The authors propose an adaptive anti-disturbance control strategy for dissolved oxygen that combines nonlinear disturbance observation with an adaptive sliding model control. Initially, a dynamic model for controlling dissolved oxygen in a recirculating water aquaculture system was developed. The model considers external disturbances like artificial oxygenation, abrupt changes in system flow, and variations in culture oxygen consumption. Secondly, to enhance the robustness and accuracy of controlling dissolved oxygen concentration, the paper introduces a nonlinear adaptive disturbance observer for real-time estimation and observation of external disturbances and system uncertainties. This is accompanied by a sliding-mode control-based adaptive anti-disturbance strategy. Lastly, the simulation results demonstrate that the control strategy proposed in this paper shows resistance to system uncertainties and unknown external disturbances. Furthermore, it reduces the model accuracy requirements for the controller and proves to be suitable for accurately controlling dissolved oxygen in circulating water systems. Full article
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16 pages, 1518 KiB  
Article
Analytical Studies on Approximate Lag and Anticipating Synchronization in Two Unidirectionally Coupled Hyperchaotic Chen Systems without Time Delay
by Li-Jun Ouyang, Bing-Qing Xie and Bin Ding
Appl. Sci. 2023, 13(21), 11949; https://doi.org/10.3390/app132111949 - 1 Nov 2023
Viewed by 834
Abstract
In this paper, approximate lag synchronization (LS) and anticipating synchronization (AS) between two unidirectionally coupled hyperchaotic Chen systems without time-delay coupling are analytically investigated. Firstly, the synchronization condition for exact LS in two unidirectionally coupled hyperchaotic Chen systems with time delay in signal [...] Read more.
In this paper, approximate lag synchronization (LS) and anticipating synchronization (AS) between two unidirectionally coupled hyperchaotic Chen systems without time-delay coupling are analytically investigated. Firstly, the synchronization condition for exact LS in two unidirectionally coupled hyperchaotic Chen systems with time delay in signal transmission is analytically obtained. Under such conditions, approximate LS and AS are discussed by replacing the true time-delay terms with their Taylor expansions up to the third order.Differently from other research studies, the condition for exact LS is derived by regarding LS as a special type of generalized synchronization (GS), which has nothing to do with the value of the time delay. It is convenient to individually change the value of the lag and anticipation time of approximate LS and AS without considering the synchronization condition. Our study shows the power of a new method for recreating the past signals or predicting the future signals of a hyperchaotic Chen system by using its current signals. The results provide a simple way to eliminate the negative effects of time delay in the signal transmission between two hyperchaotic systems. Full article
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20 pages, 27027 KiB  
Article
The Chinese Aviation Network: An Empirical Temporal Analysis on Its Structural Properties and Robustness
by Ruoshi Yang, Wei Sun, Meilong Le and Hongyan Zhang
Appl. Sci. 2023, 13(21), 11627; https://doi.org/10.3390/app132111627 - 24 Oct 2023
Viewed by 785
Abstract
Complex networks have encouraged scholars to develop an effective method for abstracting and optimizing aviation networks. However, researchers often overlook the aviation network’s temporal attribute and treat it as a static network. Aviation networks have strong temporal characteristics and the dynamic connection cannot [...] Read more.
Complex networks have encouraged scholars to develop an effective method for abstracting and optimizing aviation networks. However, researchers often overlook the aviation network’s temporal attribute and treat it as a static network. Aviation networks have strong temporal characteristics and the dynamic connection cannot be realistically described by a static network. It is necessary to more accurately and realistically represent these connections during the operation of an aviation network. This study explored temporal structures of the Chinese aviation temporal network (CATN) based on flight schedules and actual operational time data. Temporal networks based on time windows were represented to analyze the temporal topology features and robustness of the CATN. The results demonstrated the following: (1) based on the spatial-temporal aviation network, there is a morning departure peak (7:00–8:00) and an evening arrival peak at the airline hub (20:00–21:00); (2) examining the centrality of each airport in the CATN at various time intervals exposed fluctuations in their rankings, which could not be identified by a static network, and (3) the robustness of the CATN was found to be unaffected by time windows, but it displayed poor resilience against deliberate attacks, particularly when subjected to betweenness and closeness attacks, which target the network’s shortest paths. For obtaining a greater understanding of the operating situation of civil aviation, displaying the topological features and robustness of the temporal network is of great importance. Full article
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25 pages, 5764 KiB  
Article
Study on Stability of Elastic Compression Bending Bar in Viscoelastic Medium
by Xiaochun Zhang, Jianhan Hu and Shuyang Chen
Appl. Sci. 2023, 13(19), 11111; https://doi.org/10.3390/app131911111 - 9 Oct 2023
Viewed by 839
Abstract
In the southeastern coastal regions of China, thick layers of marine soft soil are widely distributed, exhibiting characteristics such as high compressibility, high porosity, low strength, high sensitivity, and easy thixotropy, and these viscoelastic behaviors of foundation soil have significant implications for elastic [...] Read more.
In the southeastern coastal regions of China, thick layers of marine soft soil are widely distributed, exhibiting characteristics such as high compressibility, high porosity, low strength, high sensitivity, and easy thixotropy, and these viscoelastic behaviors of foundation soil have significant implications for elastic compression bending bar, as evidenced by issues such as post-construction settlement of roadbeds and long-term operation deviation of bridge pile foundations. In this study, a mechanical model of an elastic bar embedded in an elastic and viscoelastic medium, fixed at the base and free at the top, is established based on the Winkler foundation assumption. The deflection function of a bar subjected to both axial force and locally distributed horizontal load is derived using the Rayleigh-Ritz method. Utilizing the elastic-viscoelastic correspondence principle, the viscoelastic medium surrounding the bar is modeled as an elastic medium in which the ground reaction coefficient varies within phase space formulation. This study provides a robust theoretical foundation for soft soil foundation engineering projects and fills a significant gap in the literature by offering a comprehensive framework for understanding displacement in elastic bars within viscoelastic media. Drawing upon the derivation of the deformation function for elastic rods within a viscoelastic medium, the findings of this research hold significant applicability across a range of domains. These include, but are not limited to, the expansion of roadways in regions characterized by coastal soft soil, as well as the monitoring of deformation and lifespan in bridge pile foundations. Full article
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21 pages, 648 KiB  
Article
Maximum Convergence Rate Control of a Switched Electrical Network with Symmetries
by Simone Fiori, Luca Ciaramicoli and Giovanni Berluti
Symmetry 2023, 15(10), 1861; https://doi.org/10.3390/sym15101861 - 3 Oct 2023
Viewed by 1013
Abstract
The purpose of the present research endeavor is to propose a novel control strategy for a DC-DC electrical converter realized as a switched circuit. The present endeavor is based on an early work by Leonard and Krishnaprasad where a prototypical DC-DC converter was [...] Read more.
The purpose of the present research endeavor is to propose a novel control strategy for a DC-DC electrical converter realized as a switched circuit. The present endeavor is based on an early work by Leonard and Krishnaprasad where a prototypical DC-DC converter was modeled as a state space dynamical system and controlled by an open-loop strategy based on Lie group theory. In this work, we shall rather introduce a closed-loop control strategy based on maximum convergence rate, study some features of the novel method, and illustrate its behavior by numerical simulations. A numerical comparison of the two methods complements the paper. The numerical comparison shows how the proposed feedback control method outperforms the static one in terms of convergence rate and resiliency against parameters mismatch. Full article
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15 pages, 3702 KiB  
Article
Dynamic Modeling of Motorized Spindle System with Unbalanced Mass and Spindle Inclination
by Dan Gu, Yufeng Xie, Shulin Liu, Yuan Wei and Jiayi Shen
Appl. Sci. 2023, 13(18), 10053; https://doi.org/10.3390/app131810053 - 6 Sep 2023
Viewed by 661
Abstract
The high-speed motorized spindle has been wildly used in the field of aerospace processing, due to its advantages such as high speed, high precision, and high efficiency. CNC machine tools used for processing aerospace products require high machining accuracy, and once the spindle [...] Read more.
The high-speed motorized spindle has been wildly used in the field of aerospace processing, due to its advantages such as high speed, high precision, and high efficiency. CNC machine tools used for processing aerospace products require high machining accuracy, and once the spindle fails, it will seriously affect the quality of product processing. Thus, it is important to study the faults of the spindle, especially the faults caused by subtle errors. In this work, a dynamic model of a spindle with unbalanced mass fault and spindle inclination fault is established, and the natural frequencies and mode shapes of the motorized spindle are calculated by using the whole transfer matrix method (WTMM). The deflections of the spindle initial end in the different situations are discussed when the two faults happen independently. The results show that the spindle end deflection of the same fault has different sensitivity at different speeds. At the third order of natural frequencies, the deflection of a motorized spindle is greatest regardless of the fault that occurs. Although the motorized spindle rotates at the same speed, different faults could cause different mode shapes. At the lower speed, when the unbalanced mass fault happens, the mode shape is in an arched shape, and while the spindle inclination fault happens, the mode shape is in a concave shape. Full article
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16 pages, 1121 KiB  
Article
Event-Triggered State Estimation for Uncertain Systems with Binary Encoding Transmission Scheme
by Zun Li, Binqiang Xue and Youyuan Chen
Mathematics 2023, 11(17), 3679; https://doi.org/10.3390/math11173679 - 26 Aug 2023
Viewed by 760
Abstract
This paper proposes an event-triggered state estimation method for parameter-uncertain systems with a binary encoding transmission scheme. Firstly, a binary encoding transmission scheme is introduced between the state estimator and the system to improve the efficiency of network communication. Secondly, an event-triggering mechanism [...] Read more.
This paper proposes an event-triggered state estimation method for parameter-uncertain systems with a binary encoding transmission scheme. Firstly, a binary encoding transmission scheme is introduced between the state estimator and the system to improve the efficiency of network communication. Secondly, an event-triggering mechanism (ETM) is designed to ensure the accuracy of state estimation and reduce the computational burden of the state estimator. At the event-triggered moments, considering the uncertainty of the system, the binary encoding transmission scheme, and the ETM, a moving horizon estimator (MHER) is designed using the robust least squares optimization method to obtain optimal state estimation. At the no-event-triggered moments, the state estimation of the system is computed based on an open-loop state estimator (OLER). Furthermore, stability analysis showed that the state estimation error of the proposed method is bounded. Finally, the practical value of the proposed in this paper is confirmed through numerical simulation. Full article
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18 pages, 2613 KiB  
Article
Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters
by Bin Zhen and Yu Zhang
Appl. Sci. 2023, 13(14), 8135; https://doi.org/10.3390/app13148135 - 12 Jul 2023
Cited by 2 | Viewed by 860
Abstract
This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations [...] Read more.
This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations on the basis of the Laplace transform method and convolution theorem, which are solved by applying the successive approximation method in the theory of integral equations. Compared with the results obtained by constructing Lyapunov functions or calculating the conditional Lyapunov exponents, the uncertain parameters and the scaling function factors considered in this paper have fewer restrictions, and the parameter update laws designed for the estimation of the uncertain parameters are simpler and easier to realize physically. Full article
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15 pages, 3584 KiB  
Article
Effect of the Dynamic Froude–Krylov Force on Energy Extraction from a Point Absorber Wave Energy Converter with an Hourglass-Shaped Buoy
by Houssein Yassin, Tania Demonte Gonzalez, Gordon Parker and David Wilson
Appl. Sci. 2023, 13(7), 4316; https://doi.org/10.3390/app13074316 - 29 Mar 2023
Cited by 1 | Viewed by 1647
Abstract
Point absorber wave energy converter (WEC) control strategies often require accurate models for maximum energy extraction. While linear models are suitable for small motions, the focus is on the nonlinear model of an hour-glass shaped buoy undergoing large vertical displacements. Closed-form expressions for [...] Read more.
Point absorber wave energy converter (WEC) control strategies often require accurate models for maximum energy extraction. While linear models are suitable for small motions, the focus is on the nonlinear model of an hour-glass shaped buoy undergoing large vertical displacements. Closed-form expressions for the static and dynamic Froude–Krylov forces are developed. It is shown that, in general, the dynamic and static forces are of similar magnitude, which is not the case for a spherical buoy. While the dynamic force reduces the amplitude of the net buoy force, its shape predicts a larger buoy response than if neglected, causing the nonlinear terms to have an even more significant effect. An input-state feedback linearizing controller is developed to show how the nonlinear model can be used in a control law. A 2.5 m buoy example is simulated to illustrate the approach of tracking an arbitrary displacement reference. For the case considered, the extracted power is 30% larger when the nonlinear dynamic FK force is used in the control law. The hourglass buoy is also compared to a spherical buoy to illustrate differences in their response to regular waves and energy extraction when using the same control laws. A spherical buoy diameter of 7.5 m was required to obtain the same power output as a 5 m tall hourglass buoy. A power-force-amplitude (PFA) metric is introduced to compare energy extraction performance and power take-off requirements. The hourglass buoy’s PFA was 13% larger than the spherical buoy implying that it can produce similar power but with less control effort. Full article
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19 pages, 6021 KiB  
Article
Dynamics Analysis and Chaos Identification of Compound Pendulum Jaw Crusher with Joint Clearance
by Shenpeng Wang, Yan Cui and Chune Wang
Appl. Sci. 2023, 13(1), 238; https://doi.org/10.3390/app13010238 - 24 Dec 2022
Cited by 1 | Viewed by 2141
Abstract
A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance is established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model. The correctness of the dynamic model is [...] Read more.
A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance is established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model. The correctness of the dynamic model is verified by MATLAB and Adams comparison simulation, and the best selection range of driving speed and clearance size is determined according to the laminating crushing theory (LCT). The effects of driving speed and clearance size on the shock and chaos phenomenon in the clearance mechanism are analyzed, as well as the vibration force applied to the foundation. The results show that, under the premise of meeting the requirements of crusher production capacity, increasing the driving speed and reducing the clearance size can weaken the shock and chaos phenomenon during the operation of the mechanism, improve the dynamic performance and enhance the operation stability, and the service life of foundation is prolonged with the stability of vibration force. Furthermore, the optimal combination of driving speed and clearance size is determined, which provides a theoretical basis for the optimization of the vibration force of the jaw crusher. Full article
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12 pages, 408 KiB  
Article
A PDE Model Approach to Formation Control of Large-Scale Mobile Sensor Networks with Boundary Uncertainties
by Xueming Qian and Baotong Cui
Axioms 2023, 12(1), 9; https://doi.org/10.3390/axioms12010009 - 22 Dec 2022
Viewed by 1040
Abstract
This paper investigates the formation problem of an array of large-scale mobile sensor networks. A new framework for the dynamic of mobile sensors as a continuum described by the parabolic system with boundary disturbance is proposed. The communication topology of agents is a [...] Read more.
This paper investigates the formation problem of an array of large-scale mobile sensor networks. A new framework for the dynamic of mobile sensors as a continuum described by the parabolic system with boundary disturbance is proposed. The communication topology of agents is a chain graph and fixed. Leader feedback laws which are designed in a manner to the boundary control of large-scale mobile sensor networks allow the mobile sensors to achieve the formation steadily. By referring to the Lyapunov functional method and employing a boundary control approach, a new protocol is established to deal with a formation problem for the large-scale mobile sensor networks. Finally, numerical examples are given to illustrate the usefulness of the results. Full article
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17 pages, 2635 KiB  
Article
Decomposition–Coordination of Double-Layer MPC for Constrained Systems
by Hongrui Wang, Pengbin Zhang, Zhijia Yang and Tao Zou
Entropy 2023, 25(1), 17; https://doi.org/10.3390/e25010017 - 22 Dec 2022
Viewed by 1230
Abstract
Large-scale industrial processes usually adopt centralized control and optimization methods. However, with the growth of the scale of industrial processes leading to increasing computational complexity, the online optimization capability of the double-layer model predictive control algorithm is challenged, exacerbating the difficulty of the [...] Read more.
Large-scale industrial processes usually adopt centralized control and optimization methods. However, with the growth of the scale of industrial processes leading to increasing computational complexity, the online optimization capability of the double-layer model predictive control algorithm is challenged, exacerbating the difficulty of the widespread implementation of this algorithm in the industry. This paper proposes a distributed double-layer model predictive control algorithm based on dual decomposition for multivariate constrained systems to reduce the computational complexity of process control. Firstly, to solve the problem that the original dual decomposition method does not apply to constrained systems, two improved dual decomposition model prediction control methods are proposed: the dual decomposition method based on the quadratic programming in the subsystem and the dual decomposition method based on constraint zones, respectively. It is proved that the latter will certainly converge to the constraint boundaries with appropriate convergence factors for the controlled variables. The online optimization ability of the proposed two methods is compared in discussion and simulation, concluding that the dual decomposition method based on the constraint zones exhibits superior online optimization ability. Further, a distributed double-layer model predictive control algorithm with dual decomposition based on constraint zones is proposed. Different from the objective function of the original dual decomposition model predictive control, the proposed algorithm’s dynamic control-layer objective function simultaneously tracks the steady-state optimization values of the controlled and manipulated variables, giving the optimal solution formulation of the optimization problem consisting of this objective function and the constraints. The algorithm proposed in this paper achieves the control goals while significantly reducing the computational complexity and has research significance for promoting the industrial implementation of double-layer model predictive control. Full article
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14 pages, 17566 KiB  
Article
Dynamical Analysis of a One- and Two-Scroll Chaotic System
by Meng Liu, Zhaoyan Wu and Xinchu Fu
Mathematics 2022, 10(24), 4682; https://doi.org/10.3390/math10244682 - 9 Dec 2022
Cited by 3 | Viewed by 1205
Abstract
In this paper, a three-dimensional (3D) autonomous chaotic system is introduced and analyzed. In the system, each equation contains a quadratic crossproduct. The system possesses a chaotic attractor with a large chaotic region. Importantly, the system can generate both one- and two-scroll chaotic [...] Read more.
In this paper, a three-dimensional (3D) autonomous chaotic system is introduced and analyzed. In the system, each equation contains a quadratic crossproduct. The system possesses a chaotic attractor with a large chaotic region. Importantly, the system can generate both one- and two-scroll chaotic attractors by choosing appropriate parameters. Some of its basic dynamical properties, such as the Lyapunov exponents, Lyapunov dimension, Poincaré maps, bifurcation diagram, and the chaotic dynamical behavior are studied by adjusting different parameters. Further, an equivalent electronic circuit for the proposed chaotic system is designed according to Kirchhoff’s Law, and a corresponding response electronic circuit is also designed for identifying the unknown parameters or monitoring the changes in the system parameters. Moreover, numerical simulations are presented to perform and complement the theoretical results. Full article
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23 pages, 2777 KiB  
Article
Online Tracking of Maneuvering Target Trajectory Based on Chaotic Time Series Prediction
by Qian Wei, Peng Su, Lin Zhou and Wentao Shi
Entropy 2022, 24(11), 1668; https://doi.org/10.3390/e24111668 - 15 Nov 2022
Cited by 1 | Viewed by 1260
Abstract
Online prediction of maneuvering target trajectory is one of the most popular research directions at present. Specifically, the primary factors balancing, between prediction accuracy and response time, will give the research substance. This paper presents an online trajectory prediction algorithm based on small [...] Read more.
Online prediction of maneuvering target trajectory is one of the most popular research directions at present. Specifically, the primary factors balancing, between prediction accuracy and response time, will give the research substance. This paper presents an online trajectory prediction algorithm based on small sample chaotic time series (OTP-SSCT). First, we optimize in terms of data breadth. The dynamic split window is built according to the motion characteristics of the maneuvering target, thus realizing trajectory segmentation and constructing a small sample chaotic time series prediction set. Second, since fully considering the motion patterns of maneuvering targets, we introduce the spatiotemporal features into the particle swarm optimization (PSO) model identification algorithm, which improves the identification sensitivity of key trajectory data points. Furthermore, we propose a feedback optimization strategy of residual compensation to correct the trajectory prediction values to improve the prediction accuracy. For the initial value sensitivity problem of the PSO model identification algorithm, we propose a new initial population strategy, which improves the effectiveness of initial parameters on model identification. Through simulation experiment analysis, it is verified that the proposed OTP-SSCT algorithm achieves better prediction accuracy and faster response time. Full article
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10 pages, 1538 KiB  
Article
Numerical Solution of Finite Kuramoto Model with Time-Dependent Coupling Strength: Addressing Synchronization Events of Nature
by Dharma Raj Khatiwada
Mathematics 2022, 10(19), 3633; https://doi.org/10.3390/math10193633 - 4 Oct 2022
Cited by 1 | Viewed by 1787
Abstract
The synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social to physical and biological systems. This phenomenon is often described mathematically by the Kuramoto model, which assumes oscillators of fixed natural frequencies connected by [...] Read more.
The synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social to physical and biological systems. This phenomenon is often described mathematically by the Kuramoto model, which assumes oscillators of fixed natural frequencies connected by an equal and uniform coupling strength, with an analytical solution possible only for an infinite number of oscillators. However, most real-life synchronization systems consist of a finite number of oscillators and are often perturbed by external fields. This paper accommodates the perturbation using a time-dependent coupling strength K(t) in the form of a sinusoidal function and a step function using 32 oscillators that serve as a representative of finite oscillators. The temporal evolution of order parameter r(t) and phases θj(t), key indicators of synchronization, are compared between the uniform and time-dependent cases. The identical trends observed in the two cases give an important indication that the synchrony persists even under the influence of external factors, something very plausible in the context of real-life synchronization events. The occasional boosting of coupling strength is also enough to keep the assembly of oscillators in a synchronized state persistently. Full article
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12 pages, 6108 KiB  
Article
Habitat Destruction and Restoration in Relation to Extinction and Survival of Species in Competitive Communities
by Kornphong Chonsiripong, Eakkapong Duangdai, Radom Pongvuthithum and Chulin Likasiri
Appl. Sci. 2022, 12(17), 8693; https://doi.org/10.3390/app12178693 - 30 Aug 2022
Viewed by 1141
Abstract
We studied the N-species competitive coexistence model with direct effect on habitat destruction to analyze the behaviors of abundant and extinct species in the system caused by habitat loss. The nontrivial equilibrium points of the system are determined for a general habitat destruction [...] Read more.
We studied the N-species competitive coexistence model with direct effect on habitat destruction to analyze the behaviors of abundant and extinct species in the system caused by habitat loss. The nontrivial equilibrium points of the system are determined for a general habitat destruction function. For the trivial equilibrium, species that survived the habitat destruction are identified using eigenvalues of the Jacobian matrix. Solutions of the system are also presented using the recursive method. Three special cases of habitat destruction functions are addressed: continuous destruction, which is a typical habitat destruction; sudden habitat destruction, which is similar to natural phenomena such as earthquakes or floods; and sudden habitat destruction with aftershocks. The proportional abundances of 50 species are numerically portrayed in each case. We found that the survival of a species is guaranteed if its corresponding eigenvalue is positive. However, the fact that a species has negative corresponding eigenvalue does not guarantee its extinction, as this also depends on the initial number of that species. Full article
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16 pages, 411 KiB  
Article
Dynamics of Information Flow between the Chinese A-Share Market and the U.S. Stock Market: From the 2008 Crisis to the COVID-19 Pandemic Period
by Chun-Xiao Nie and Jing Xiao
Entropy 2022, 24(8), 1102; https://doi.org/10.3390/e24081102 - 10 Aug 2022
Cited by 2 | Viewed by 1456
Abstract
The relationship between the Chinese market and the US market is widely concerned by researchers and investors. This paper uses transfer entropy and local random permutation (LRP) surrogates to detect the information flow dynamics between two markets. We provide [...] Read more.
The relationship between the Chinese market and the US market is widely concerned by researchers and investors. This paper uses transfer entropy and local random permutation (LRP) surrogates to detect the information flow dynamics between two markets. We provide a detailed analysis of the relationship between the two markets using long-term daily and weekly data. Calculations show that there is an asymmetric information flow between the two markets, in which the US market significantly affects the Chinese market. Dynamic analysis based on weekly data shows that the information flow evolves, and includes three significant periods between 2004 and 2021. We also used daily data to analyze the dynamics of information flow in detail over the three periods and found that changes in the intensity of information flow were accompanied by major events affecting the market, such as the 2008 financial crisis and the COVID-19 pandemic period. In particular, we analyzed the impact of the S&P500 index on different industry indices in the Chinese market and found that the dynamics of information flow exhibit multiple patterns. This study reveals the complex information flow between two markets from the perspective of nonlinear dynamics, thereby helping to analyze the impact of major events and providing quantitative analysis tools for investment practice. Full article
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15 pages, 2152 KiB  
Article
Integral Non-Singular Terminal Sliding Mode Consensus Control for Multi-Agent Systems with Disturbance and Actuator Faults Based on Finite-Time Observer
by Pu Yang, Yu Ding, Ziwei Shen and Kejia Feng
Entropy 2022, 24(8), 1068; https://doi.org/10.3390/e24081068 - 2 Aug 2022
Cited by 3 | Viewed by 1895
Abstract
This paper studies the consensus fault-tolerant control problem of a class of second-order leader–follower multi-agent systems with unknown disturbance and actuator faults, and proposes an integral non-singular terminal sliding mode control algorithm based on a finite-time observer. First, a finite-time disturbance observer was [...] Read more.
This paper studies the consensus fault-tolerant control problem of a class of second-order leader–follower multi-agent systems with unknown disturbance and actuator faults, and proposes an integral non-singular terminal sliding mode control algorithm based on a finite-time observer. First, a finite-time disturbance observer was designed based on a combination of high-order sliding mode and dual layers adaptive rules to realize fast estimation and compensation of disturbance and faults. Then, a sliding surface with additional integral links was designed based on the conventional sliding surface, and an integral non-singular terminal sliding mode controller is proposed to realize the robust consensus in finite time and accurately diminish the chattering phenomena. Finally, a numerical example and simulation verify the effectiveness. Full article
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