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Mathematics
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Nonlinear Dynamics and Control: Challenges and Innovations
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Nonlinear Dynamics and Control: Challenges and Innovations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 1 July 2025 | Viewed by 3516

Special Issue Editor

Dr. Ning Cai

E-Mail Website
Guest Editor
Department of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing 100876, China
Interests: complex dynamical system; robust control of nonlinear systems

Special Issue Information

Dear Colleagues,

Nonlinear dynamics and control are fundamental aspects of scientific inquiry and have far-reaching implications across a wide range of disciplines. From engineering and physics to biology and social sciences, nonlinear systems pervade our understanding of the world around us. This Special Issue will provide an invaluable platform to delve into the challenges faced in comprehending, analyzing, and controlling nonlinear systems, while also presenting novel approaches and innovative techniques that push the boundaries of current knowledge.

We seek high-quality contributions that illuminate the multifaceted aspects of nonlinear dynamics and control. Authors are encouraged to explore topics such as nonlinear control theory and applications, the application of chaos theory in control systems, nonlinear dynamics and stability analysis, bifurcation analysis and control, complex networks and their control, nonlinear time series analysis and prediction, dynamical systems and their control in engineering and physics, nonlinear control in biological and ecological systems, the role of nonlinear dynamics in social sciences and economics, as well as the use of nonlinear control in robotics and automation.

Dr. Ning Cai
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex dynamical system
  • nonlinear Dynamics
  • control theory
  • nonlinear systems

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Published Papers (4 papers)

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Research

19 pages, 1501 KiB  
Article
Frequency and Buckling Analysis of FG Beams with Asymmetric Material Distribution and Thermal Effect
by Xiaokang Du, Liang Yin, Xian Guo, Yuanzhao Chen, Liang Li, Dingguo Zhang and Sijia Chen
Mathematics 2025, 13(5), 826; https://doi.org/10.3390/math13050826 - 1 Mar 2025
Viewed by 540
Abstract
The frequency and buckling characteristics of functional gradient (FG) beams with asymmetric material distribution in the temperature field are analyzed in this paper. Generally, the asymmetrical material distribution of FG beams results in a non-zero neutral axis and non-zero thermal moment. However, some [...] Read more.
The frequency and buckling characteristics of functional gradient (FG) beams with asymmetric material distribution in the temperature field are analyzed in this paper. Generally, the asymmetrical material distribution of FG beams results in a non-zero neutral axis and non-zero thermal moment. However, some previous studies adopted the treatment of homogeneous beams in which the neutral axis and thermal moment were set as zero. To this end, a comprehensive FG beam model with thermal effect is developed based on the absolute nodal coordinate formulation, in which Euler–Bernoulli beam theory, Lagrangian strain, exact curvature, thermally induced strain, and neutral axis position are considered. For the convenience of comparisons, the presented model can be simplified into three models which do not consider the neutral axis or thermal moment. The numerical results indicate that the influence of the neutral axis on the thermal axial force is minimal while that on the thermal moment is significant. In the case of the high temperature difference, frequency, critical temperature difference, unstable state, and the buckling type of the FG beams are misjudged when the neutral axis or thermal moment is ignored. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control: Challenges and Innovations)
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16 pages, 3371 KiB  
Article
Exploring Chaos and Stability in a 3-D Finance Model with Absolute Function Nonlinearity
by Muhamad Deni Johansyah, Sundarapandian Vaidyanathan, Khaled Benkouider, Aceng Sambas, Kandimalla Mallikarjuna Rao and Katuru Anjaneyulu
Mathematics 2025, 13(5), 735; https://doi.org/10.3390/math13050735 - 24 Feb 2025
Viewed by 304
Abstract
This paper introduces a novel chaotic finance system derived by incorporating a modeling uncertainty with an absolute function nonlinearity into existing financial systems. The new system, based on the works of Gao and Ma, and Vaidyanathan et al., demonstrates enhanced chaotic behavior with [...] Read more.
This paper introduces a novel chaotic finance system derived by incorporating a modeling uncertainty with an absolute function nonlinearity into existing financial systems. The new system, based on the works of Gao and Ma, and Vaidyanathan et al., demonstrates enhanced chaotic behavior with a maximal Lyapunov exponent (MLE) of 0.1355 and a fractal Lyapunov dimension of 2.3197. These values surpass those of the Gao-Ma system (MLE = 0.0904, Lyapunov dimension = 2.2296) and the Vaidyanathan system (MLE = 0.1266, Lyapunov dimension = 2.2997), signifying greater complexity and unpredictability. Through parameter analysis, the system transitions between periodic and chaotic regimes, as confirmed by bifurcation diagrams and Lyapunov exponent spectra. Furthermore, multistability is demonstrated with coexisting chaotic attractors for p = 0.442 and periodic attractors for p = 0.48. The effects of offset boosting control are explored, with attractor positions adjustable by varying a control parameter k, enabling transitions between bipolar and unipolar chaotic signals. These findings underline the system’s potential for advanced applications in secure communications and engineering, providing a deeper understanding of chaotic finance models. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control: Challenges and Innovations)
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14 pages, 292 KiB  
Article
Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions
by Zhiyuan Yuan, Luyao Wang, Wenchang He, Ning Cai and Jia Mu
Mathematics 2024, 12(12), 1877; https://doi.org/10.3390/math12121877 - 16 Jun 2024
Viewed by 1040
Abstract
We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, [...] Read more.
We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by using fixed-point theorems, we establish the existence of mild solutions under more relaxed conditions. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control: Challenges and Innovations)
20 pages, 1208 KiB  
Article
Event-Triggered Adaptive Neural Prescribed Performance Tracking Control for Nonlinear Cyber–Physical Systems against Deception Attacks
by Chunyan Li, Yinguang Li, Jianhua Zhang and Yang Li
Mathematics 2024, 12(12), 1838; https://doi.org/10.3390/math12121838 - 13 Jun 2024
Cited by 2 | Viewed by 1123
Abstract
This paper investigates the problem of the adaptive neural network tracking control of nonlinear cyber–physical systems (CPSs) subject to unknown deception attacks with prescribed performance. The considered system is under the influence of unknown deception attacks on both actuator and sensor networks, making [...] Read more.
This paper investigates the problem of the adaptive neural network tracking control of nonlinear cyber–physical systems (CPSs) subject to unknown deception attacks with prescribed performance. The considered system is under the influence of unknown deception attacks on both actuator and sensor networks, making the research problem challenging. The outstanding contribution of this paper is that a new anti-deception attack-prescribed performance tracking control scheme is proposed through a special coordinate transformation and funnel function, combined with backstepping and bounded estimation methods. The transient performance of the system can be ensured by the prescribed performance control scheme, which makes the indicators of the controlled system, such as settling time and tracking accuracy, able to be pre-assigned offline according to the task needs, and the applicability of the prescribed performance is tested by selecting different values of the settling time (0.5 s, 1 s, 1.5 s, 2 s, 2.5 s, and 3 s). In addition, to save the computational and communication resources of the CPS, this paper uses a finite-time differentiator to approximate the virtual control law differentiation to avoid “complexity explosion” and a switching threshold event triggering mechanism to save the communication resources for data transmission. Finally, the effectiveness of the proposed control strategy is further verified by an electromechanical system simulation example. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control: Challenges and Innovations)
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