Search Results (1,225)

In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear partial differential equation that integrates additional spatial and dispersive effects to extend the concepts to more intricate wave dynamics, relevant in engineering and science for understanding complex phenomena. To examine the solitary wave solutions of the proposed model, we employ sophisticated analytical techniques, including the generalized projective Riccati equation method, the new improved generalized exponential rational function method, and the modified F-expansion method, along with mathematical simulations, to obtain a deeper insight into wave propagation. To explore desirable soliton solutions, the nonlinear partial differential equation is converted into its respective ordinary differential equations by wave transforms utilizing $\beta$-fractional derivatives. Further, the solutions in the forms of bright, dark, singular, combined, and complex solitons are secured. Various physical parameter values and arrangements are employed to investigate the soliton solutions of the system. Variations in parameter values result in specific behaviors of the solutions, which we illustrate via various types of visualizations. Additionally, a key aspect of this research involves analyzing the chaotic behavior of the governing model. A perturbed version of the system is derived and then analyzed using chaos detection techniques such as power spectrum analysis, Poincaré return maps, and basin attractor visualization. The study of nonlinear dynamics reveals the system’s sensitivity to initial conditions and its dependence on time-decay effects. This indicates that the system exhibits chaotic behavior under perturbations, where even minor variations in the starting conditions can lead to drastically different outcomes as time progresses. Such behavior underscores the complexity and unpredictability inherent in the system, highlighting the importance of understanding its chaotic dynamics. This study evaluates the effectiveness of currently employed methodologies and elucidates the specific behaviors of the system’s nonlinear dynamics, thus providing new insights into the field of high-dimensional nonlinear scientific wave phenomena. The results demonstrate the effectiveness and versatility of the approach used to address complex nonlinear partial differential equations. Full article

This article concerns a Cournot duopoly game with homogeneous expectations. The cost functions of the two players are assumed to be asymmetric to capture possible asymmetries in firms’ technologies or firms’ input costs. Large values of the speed of adjustment of the players destabilize the Nash Equilibrium (N.E.) and cause the appearance of a chaotic trajectory in the Discrete Dynamical System (D.D.S.). The scope of this article is to control the chaotic dynamics that appear outside the stability field, assuming asymmetric cost functions of the two players. Specifically, one player uses linear costs, while the other uses nonlinear costs (quadratic or cubic). The cubic cost functions are widely used in the Economic Dispatch Problem. The delayed feedback control method is applied by introducing a new control parameter at the D.D.S. It is shown that larger values of the control parameter keep the N.E. locally asymptotically stable even for higher values of the speed of adjustment. Full article

This study investigates the nonlinear aeroelastic behavior and energy harvesting performance of a two-degrees-of-freedom NACA 0012 airfoil under varying reduced velocities and electrical load resistances. The system exhibits a range of dynamic responses, including periodic and chaotic states, governed by strong fluid–structure interactions. Nonlinear oscillations first appear near the critical reduced velocity $U_r^{*}=6$, with large-amplitude limit-cycle oscillations emerging around $U_r^{*}=8$ in the absence of the electrical loading. As the load resistance increases, this transition shifts to higher $U_r^{*}$, reflecting the damping effect of the electrical load. Fourier spectra reveal the presence of odd and even superharmonics in the lift coefficient, indicating nonlinearities induced by fluid–structure coupling, which diminishes at higher resistances. Phase portraits and Poincaré maps capture transitions across dynamical regimes, from periodic to chaotic behavior, particularly at a low resistance. The voltage output correlates with variations in the lift force, reaching its maximum at an intermediate resistance before declining due to a suppressing nonlinearity. Flow visualizations identify various vortex shedding patterns, including single (S), paired (P), triplet (T), multiple-pair (mP) and pair with single (P + S) that weaken at higher resistances and reduced velocities. The results demonstrate that nonlinearity plays a critical role in efficient voltage generation but remains effective only within specific parameter ranges. Full article

In this paper, an exponential delay feedback method is proposed to improve the performance of the digital chaotic maps against their dynamical degradation. In this paper, the performance of the scheme is verified using one-dimensional linear, exponential, and nonlinear exponential, Logistic, and Chebyshev maps, and numerical analyses show that the period during which the chaotic sequence enters the cycle is considerably prolonged, and the correlation performance is improved. At the same time, in order to verify the practicality of the method, an image encryption algorithm is designed, and its security analysis results show that the algorithm has a high level of security and can compete with other encryption schemes. Therefore, the exponential delay feedback method can effectively improve the dynamics degradation of a digital chaotic map. Full article

As a core component of automated logistics systems, delivery robots hold significant application value in the field of unmanned delivery. This research addresses the robot path planning problem, aiming to enhance delivery efficiency and reduce operational costs through systematic improvements to the RIME optimization algorithm. Through in-depth analysis, we identified several major drawbacks in the standard RIME algorithm for path planning: insufficient global exploration capability in the initial stages, a lack of diversity in the hard RIME search mechanism, and oscillatory phenomena in soft RIME step size adjustment. These issues often lead to undesirable phenomena in path planning, such as local optima traps, path redundancy, or unsmooth trajectories. To address these limitations, this study proposes the Multi-Strategy Controlled Rime Algorithm (MSRIME), whose innovation primarily manifests in three aspects: first, it constructs a multi-strategy collaborative optimization framework, utilizing an infinite folding Fuch chaotic map for intelligent population initialization to significantly enhance the diversity of solutions; second, it designs a cooperative mechanism between a controlled elite strategy and an adaptive search strategy that, through a dynamic control factor, autonomously adjusts the strategy activation probability and adaptation rate, expanding the search space while ensuring algorithmic convergence efficiency; and finally, it introduces a cosine annealing strategy to improve the step size adjustment mechanism, reducing parameter sensitivity and effectively preventing path distortions caused by abrupt step size changes. During the algorithm validation phase, comparative tests were conducted between two groups of algorithms, demonstrating their significant advantages in optimization capability, convergence speed, and stability. Further experimental analysis confirmed that the algorithm’s multi-strategy framework effectively suppresses the impact of coordinate and dimensional differences on path quality during iteration, making it more suitable for delivery robot path planning scenarios. Ultimately, path planning experimental results across various Building Coverage Rate (BCR) maps and diverse application scenarios show that MSRIME exhibits superior performance in key indicators such as path length, running time, and smoothness, providing novel technical insights and practical solutions for the interdisciplinary research between intelligent logistics and computer science. Full article

Aiming at the problem that the aggravation of the wheel tread wear of high-speed trains leads to the deterioration of train operation performance and an increase in re-profiling times, a multi-objective data-driven optimization design method for the wheel profile is proposed. Firstly, the chaotic map is introduced into the population initialization process of the golden jackal algorithm. In the later stage of the algorithm iteration, random disturbance is introduced with optimization algebra as the switching condition to obtain an improved optimization algorithm, and the performance index of the optimization algorithm is verified to be superior to other algorithms. Secondly, the improved multi-objective optimization algorithm and data-driven model are used to optimize the tread coordinates and obtain an optimized profile. The vehicle dynamics performance of the optimized profile and the wheel wear evolution after long-term service are compared. The results show that the tread wear index of the left and right wheels in a straight line is reduced by 62.4% and 62.6%, respectively, and the wear index of the left and right wheels in a curved line is reduced by 26.5% and 5.5%, respectively. The stability and curve passing performance of the optimized profile are improved. Under the long-term service conditions of the train, the wear amount of the optimized profile is greatly reduced. After the wear prediction of 200,000 km, the wear amount of the optimized profile is reduced by 60.1%, and it has better curve-passing performance. Full article

This study develops a dynamic IS-LM macroeconomic model that incorporates delayed taxation and a memory-dependent income effect, and calibrates it to quarterly data for Romania (2000–2023). Within this framework, fiscal policy lags are modelled using a “memory” income variable that weights past incomes, an approach grounded in distributed lag theory to capture how historical economic conditions influence current dynamics. The model is analysed both analytically and through numerical simulations. We derive stability conditions and employ bifurcation analysis to explore how the timing of taxation influences macroeconomic equilibrium. The findings reveal that an immediate taxation regime yields a stable adjustment toward a unique equilibrium, consistent with classical IS-LM expectations. In contrast, delayed taxation, where tax revenue depends on past income, can destabilise the system, giving rise to cycles and even chaotic fluctuations for parameter values that would be stable under immediate collection. In particular, delays act as a destabilising force, lowering the threshold of the output-adjustment speed at which oscillations emerge. These results highlight the critical importance of policy timing: prompt fiscal feedback tends to stabilise the economy, whereas lags in fiscal intervention can induce endogenous cycles. The analysis offers policy-relevant insights, suggesting that reducing fiscal response delays or counteracting them with other stabilisation tools is crucial for macroeconomic stability. Full article

The spread of computer viruses represents a major challenge to digital security, underscoring the need for a deeper understanding of their propagation mechanisms. This study examines the stability and chaotic dynamics of a fractional discrete Susceptible-Infected (SI) model for computer viruses, incorporating commensurate and incommensurate types of fractional orders. Using the basic reproduction number $R_0$, the derivation of stability conditions is followed by an investigation of how varying fractional orders affect the system’s behavior. To explore the system’s nonlinear chaotic behavior, the research of this study employs a suite of analytical tools, including the analysis of bifurcation diagrams, phase portraits, and the evaluation of the maximum Lyapunov exponent (MLE) for the study of chaos. The model’s complexity is confirmed through advanced complexity algorithms, including spectral entropy, approximate entropy, and the $0-1$ test. These measures offer a more profound insight into the complex behavior of the system and the role of fractional order. Numerical simulations provide visual evidence of the distinct dynamics associated with commensurate and incommensurate fractional orders. These results provide insights into how fractional derivatives influence behaviors in cyberspace, which can be leveraged to design enhanced cybersecurity measures. Full article

A four-vector potential of an external test electromagnetic field in a Schwarzschild background is described in terms of a combination of dipole and quadrupole magnetic fields. This combination is an interior solution of the source-free Maxwell equations. Such external test magnetic fields cause the dynamics of charged particles around the black hole to be nonintegrable, and are mainly responsible for chaotic dynamics of charged particles. In addition to the external magnetic fields, some circumstances should be required for the onset of chaos. The effect of the magnetic fields on chaos is shown clearly through an explicit symplectic integrator and a fast Lyapunov indicator. The inclusion of the quadrupole magnetic fields easily induces chaos, compared with that of the dipole magnetic fields. This result is because the Lorentz forces from the quadrupole magnetic fields are larger than those from the dipole magnetic fields. In addition, the Lorentz forces act as attractive forces, which are helpful for bringing the occurrence of chaos in the nonintegrable case. Full article

Spatiotemporal correlations between meteo-inputs and wind–solar outputs in an optimal regional scale are crucial for developing robust models, reliable in mid-term prediction time horizons. Modelling border conditions is vital for early recognition of progress in chaotic atmospheric processes at the destination of interest. This approach is used in differential and deep learning; artificial intelligence (AI) techniques allow for reliable pattern representation in long-term uncertainty and regional irregularities. The proposed day-by-day estimation of the RE production potential is based on first data processing in detecting modelling initialisation times from historical databases, considering correlation distance. Optimal data sampling is crucial for AI training in statistically based predictive modelling. Differential learning (DfL) is a recently developed and biologically inspired strategy that combines numerical derivative solutions with neurocomputing. This hybrid approach is based on the optimal determination of partial differential equations (PDEs) composed at the nodes of gradually expanded binomial trees. It allows for modelling of highly uncertain weather-related physical systems using unstable RE. The main objective is to improve its self-evolution and the resulting computation in prediction time. Representing relevant patterns by their similarity factors in input–output resampling reduces ambiguity in RE forecasting. Node-by-node feature selection and dynamical PDE representation of DfL are evaluated along with long-short-term memory (LSTM) recurrent processing of deep learning (DL), capturing complex spatio-temporal patterns. Parametric C++ executable software with one-month spatial metadata records is available to compare additional modelling strategies. Full article

This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness against disturbance in wireless environments. To be applied to embedded microprocessors, the continuous-time chaotic system is discretized using the Grunwald–Letnikov approximation. To avoid the loss of generality of chaotic behavior, Lyapunov exponents are computed to validate the preservation of chaos in the discrete-time domain. The FBELNN controller is then developed to synchronize two non-identical chaotic systems under different initial conditions, enabling secure data encryption and decryption. Additionally, the DOB is introduced to estimate and mitigate the effects of bounded uncertainties and external disturbances, enhancing the system’s resilience to stealthy attacks. The proposed control structure is experimentally implemented on a wireless communication system utilizing ESP32 microcontrollers (Espressif Systems, Shanghai, China) based on the ESP-NOW protocol. Both control and feedback signals of the electric drive system are encrypted using chaotic states, and real-time decryption at the receiver confirms system integrity. Experimental results verify the effectiveness of the proposed method in achieving robust synchronization, accurate signal recovery, and a reliable wireless control system. The combination of FBELNN and DOB demonstrates significant potential for real-time, low-cost, and secure applications in smart electric drive systems and industrial automation. Full article

The deep integration of smart grid and Internet of Things technologies has made high-speed power line carrier communication a key communication technology in energy management, industrial monitoring, and smart home applications, owing to its advantages of requiring no additional wiring and offering wide coverage. However, the inherent characteristics of power line channels, such as strong noise, multipath fading, and time-varying properties, pose challenges to traditional encryption algorithms, including low key distribution efficiency and weak anti-interference capabilities. These issues become particularly pronounced in high-speed transmission scenarios, where the conflict between data security and communication reliability is more acute. To address this problem, a secure transmission method for high-speed power line carrier communication based on generalized two-dimensional polynomial chaotic mapping is proposed. A high-speed power line carrier communication network is established using a power line carrier routing algorithm based on the minimal connected dominating set. The autoregressive moving average model is employed to determine the degree of transmission fluctuation deviation in the high-speed power line carrier communication network. Leveraging the complex dynamic behavior and anti-decoding capability of generalized two-dimensional polynomial chaotic mapping, combined with the deviation, the communication key is generated. This process yields encrypted high-speed power line carrier communication ciphertext that can resist power line noise interference and signal attenuation, thereby enhancing communication confidentiality and stability. By applying reference modulation differential chaotic shift keying and integrating the ciphertext of high-speed power line carrier communication, a secure transmission scheme is designed to achieve secure transmission in high-speed power line carrier communication. The experimental results demonstrate that this method can effectively establish a high-speed power line carrier communication network and encrypt information. The maximum error rate obtained by this method is 0.051, and the minimum error rate is 0.010, confirming its ability to ensure secure transmission in high-speed power line carrier communication while improving communication confidentiality. Full article

This theoretical research study proposes a novel hybrid algorithm that integrates an improved quasi-dynamical oppositional learning mutation scheme into the Mountain Gazelle Optimization method, augmented with chaotic sequences, for the thermal and economical design of a shell-and-tube heat exchanger operating with nanofluids. The Mountain Gazelle Optimizer is a recently developed metaheuristic algorithm that simulates the foraging behaviors of Mountain Gazelles. However, it suffers from premature convergence due to an imbalance between its exploration and exploitation mechanisms. A two-step improvement procedure is implemented to enhance the overall search efficiency of the original algorithm. The first step concerns substituting uniformly random numbers with chaotic numbers to refine the solution quality to better standards. The second step is to develop a novel manipulation equation that integrates different variants of quasi-dynamic oppositional learning search schemes, guided by a novel intelligently devised adaptive switch mechanism. The efficiency of the proposed algorithm is evaluated using the challenging benchmark functions from various CEC competitions. Finally, the thermo-economic design of a shell-and-tube heat exchanger operated with different nanoparticles is solved by the proposed improved metaheuristic algorithm to obtain the optimal design configuration. The predictive results indicate that using water + SiO₂ instead of ordinary water as the refrigerant on the tube side of the heat exchanger reduces the total cost by 16.3%, offering the most cost-effective design among the configurations compared. These findings align with the demonstration of how biologically inspired metaheuristic algorithms can be successfully applied to engineering design. Full article

With the large-scale application and high-quality development demands of optical fiber cables, higher requirements have been placed on the corresponding measurement technologies. In recent years, optical fiber testing has played a crucial role in evaluating cable performance, as well as in the deployment, operation, maintenance, fault repair, and upgrade of optical networks. The Optical Time-Domain Reflectometer (OTDR) is a fiber fault diagnostic tool recommended by standards such as the International Telecommunication Union and the International Electrotechnical Commission. It is used to certify the performance of new fiber links and monitor the status of existing ones, detecting and locating fault events with advantages including simple operation, rapid response, and cost-effectiveness. First, this paper introduces the working principle and system architecture of OTDR, along with a brief discussion of its performance evaluation metrics. Next, a comprehensive review of improved OTDR technologies and systems is provided, categorizing different performance enhancement methods, including the enhanced measurement distance with simple structure and low cost in 2024, and the high spatial resolution measurement of optical fiber reflection events and non-reflection events in 2025. Finally, the development trends and future research directions of OTDR are outlined, aiming to achieve the development of low-cost, high-performance OTDR systems. Full article

In medical diagnostics, brain tumor classification remains essential, as accurate and efficient models aid medical professionals in early detection and treatment planning. Deep learning methodologies for brain tumor classification have gained popularity due to their potential to deliver prompt and precise diagnostic results. This article proposes a novel classification technique that integrates the Xception model with a hybrid attention mechanism and progressive image resizing to enhance performance. The methodology is built on a combination of preprocessing techniques, transfer learning architecture reconstruction, and dynamic fine-tuning strategies. To optimize key hyper-parameters, this study employed the Dynamic Chaotic Whale Optimization Algorithm. Additionally, we developed a novel learning rate scheduler that dynamically adjusts the learning rate based on image size at each training phase, improving training efficiency and model adaptability. Batch sizes and layer freezing methods were also adjusted according to image size. We constructed an ensemble approach by preserving models trained on different image sizes and merging their results using weighted averaging, bagging, boosting, stacking, blending, and voting techniques. Our proposed method was evaluated on benchmark datasets achieving remarkable accuracies of 99.67%, 99.09%, and 99.67% compared to the classical algorithms. Full article