Search Results (77)

This paper presents a detailed study of the $(3+1)$-dimensional Zakharov–Kuznetsov–Burgers equation to investigate shock-wave phenomena in dusty plasmas with quantum effects. The model provides significant physical insight into nonlinear dispersive and dissipative structures arising in charged-dust–ion environments, corresponding to both laboratory and astrophysical plasmas. We then perform a qualitative, numerically assisted dynamical analysis using bifurcation diagrams, multistability checks, return maps, Poincaré sections, and phase portraits. For both the unperturbed and a perturbed system, we identify chaotic, quasi-periodic, and periodic regimes from these numerical diagnostics; accordingly, our dynamical conclusions are qualitative. We also examine frequency-response and time-delay sensitivity, providing a qualitative classification of nonlinear behavior across a broad parameter range. After establishing the global dynamical picture, traveling-wave solutions are obtained using the Paul–Painlevé approach. These solutions represent shock and solitary structures in the plasma system, thereby bridging the analytical and dynamical perspectives. The significance of this study lies in combining a detailed dynamical framework with exact traveling-wave solutions, allowing a deeper understanding of nonlinear shock dynamics in quantum dusty plasmas. These results not only advance theoretical plasma modeling but also hold potential applications in plasma-based devices, wave propagation in optical fibers, and astrophysical plasma environments. Full article

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article

Boolean chaotic systems solely composed of logic devices have been successfully applied in fields such as random number generation, reservoir computing, and radar detection because of their simple structure and amenability to integration. However, noise in a circuit makes Boolean chaotic systems less robust, which means noise transforms the outputs from chaotic to periodic. In this paper, the characteristics of the process through which logic devices respond to input signals are called device response characteristics. A device’s response characteristic parameters can adjust its response speed and the results it yields to the same input signal. The relationship between logical device response characteristic parameters and the time delay parameter was studied. The results indicate that the distribution range and continuity of chaos in the time delay parameter space can be enhanced by reducing the logical device response characteristic parameters, thereby improving the robustness of a Boolean chaotic system. This research is significant for the hardware design of Boolean chaotic system, as it details the selection of appropriate devices for enhancing chaotic time delay parameter space and robustness. Full article

With the growing demand for secure image communication, effective encryption solutions are critical for safeguarding visual data from unauthorized access. The substitution box (S-box) in AES (Advanced Encryption Standard) is critical for ensuring nonlinearity and security. However, the static S-box used in AES is vulnerable to algebraic attacks, side-channel attacks, and so on. This study offers a novel Lorenz key and Chua key-based Reversible Substitution Box (LCK-SB) for image encryption, which takes advantage of the chaotic behavior of the Lorenz and Chua key systems to improve security due to nonlinear jumps and mixed chaotic behavior while maintaining optimal quantum cost, area, and power. The suggested method uses a hybrid Lorenz and Chua key generator to create a highly nonlinear and reversible S-box, which ensures strong confusion and diffusion features. The performance of the LCK-SB approach is examined on field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) platforms, and the findings show that quantum cost, delay, and power are decreased by 97%, 74.6%, and 35%, respectively. Furthermore, the formal security analysis shows that the suggested technique efficiently resists threats. The theoretical analysis and experimental assessment show that the suggested system is more secure for picture encryption, making it suitable for real-time and high-security applications. 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

To address the conflicting demands of the energy crisis, environmental pollution, and economic growth, the electric vehicle (EV) industry has expanded rapidly, facilitating the widespread adoption of power batteries. This paper investigates the use of chaos theory and machine learning for predicting the remaining useful life (RUL) of lithium-ion batteries. Firstly, the mutual information method determines the time delay of the monitoring sequence, while the improved false nearest neighbor method (Cao algorithm) establishes the embedding dimension, yielding the phase space reconstruction parameters. Secondly, the maximum Lyapunov exponent identifies the chaotic properties of the capacity decay time series, and a prediction dataset is constructed based on phase space reconstruction theory. Finally, leveraging the chaotic time-series features, a support vector machine (SVM) model is developed for lithium-ion battery RUL prediction. The algorithm is subsequently validated through simulation using the NASA battery dataset. The results demonstrate that the proposed method achieves high predictive accuracy and stability, providing reliable RUL estimates for the battery management system (BMS). Full article

Neural network (NN)-based controllers have emerged as a paradigm-shifting approach in modern control systems, demonstrating unparalleled capabilities in governing nonlinear dynamical systems with inherent uncertainties. This comprehensive review systematically investigates the theoretical foundations and practical implementations of NN controllers through the prism of Lyapunov stability theory, NN controller frameworks, and robustness analysis. The review establishes that recurrent neural architectures inherently address time-delayed state compensation and disturbance rejection, achieving superior trajectory tracking performance compared to classical control strategies. By integrating imitation learning with barrier certificate constraints, the proposed methodology ensures provable closed-loop stability while maintaining safety-critical operation bounds. Experimental evaluations using chaotic system benchmarks confirm the exceptional modeling capacity of NN controllers in capturing complex dynamical behaviors, complemented by formal verification advances through reachability analysis techniques. Practical demonstrations in aerial robotics and intelligent transportation systems highlight the efficacy of controllers in real-world scenarios involving environmental uncertainties and multi-agent interactions. The theoretical framework synergizes data-driven learning with nonlinear control principles, introducing hybrid automata formulations for transient response analysis and adjoint sensitivity methods for network optimization. These innovations position NN controllers as a transformative technology in control engineering, offering fundamental advances in stability-guaranteed learning and topology optimization. Future research directions will emphasize the integration of physics-informed neural operators for distributed control systems and event-triggered implementations for resource-constrained applications, paving the way for next-generation intelligent control architectures. Full article

It is vital to study the stability of power systems under small perturbations to prevent blackouts. This study presents a load-shedding strategy that has been incorporated within the swing equation to reduce instability and delay the onset of chaotic dynamics. The objective of this study was to identify the minimal load reductions required after disturbances to maintain the frequency above a critical value. Analytical techniques such as eigenvalue analysis and perturbation methods can also be supported with numerical simulations using bifurcation diagrams, Lyapunov exponents, and the Simulink model. When compared to the conventional stepwise load-shedding method, the proposed approach allows for dynamic adjustments and presents a 49% increase in stable regions and a 45% reduction in recovery time. Performance was also analysed under different damping, inertia, and load scenarios. These results suggest that the strategy demonstrated in this research provides a robust and computationally practical solution for modern power system applications. Full article

In this paper, a novel fractional-order chaotic system equipped with symmetric attractors was proposed for the full-coverage path-planning problem of mobile robots, especially in application scenarios where path privacy needs to be protected. By coupling this system with a kinematic model of a mobile robot, a novel path-planning algorithm was designed to realize encrypted full-coverage path planning. A predefined time-synchronization control strategy effectively resolved inconsistencies in the path caused by initial position, time delay, and uncertain disturbances. Numerical simulation results demonstrated that the proposed path-planning method, based on the novel chaotic system, significantly improved coverage and randomness, compared to existing studies. Moreover, it maintained accuracy and stability in path planning, even in the presence of time delays and uncertain disturbances. Full article

Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order (FO) nonlinear systems under these two practical constraints. Two primary methodologies are employed: the vector Lyapunov function method, integrated with the M-matrix approach, and the second one is the Lyapunov-like function method, which incorporates diffusive realization and the Lipchitz condition. An optimization framework is proposed to design stabilizing controllers based on the derived stability conditions. The proposed methods are validated numerically through their application to the FO Lorenz and Liu systems, demonstrating their effectiveness in handling actuator saturation and time delay. Full article

Anguilliform locomotion, an efficient aquatic locomotion mode where the whole body is engaged in fluid–body interaction, contains sophisticated physics. We hypothesized that data-driven modeling techniques may extract models or patterns of the swimmers’ dynamics without implicitly measuring the hydrodynamic variables. This work proposes empirical kinematic control and data-driven modeling of a soft swimming robot. The robot comprises six serially connected segments that can individually bend with the segmental pneumatic artificial muscles. Kinematic equations and relations are proposed to measure the desired actuation to mimic anguilliform locomotion kinematics. The robot was tested experimentally and the position and velocities of spatially digitized points were collected using QualiSys^® Tracking Manager (QTM) 1.6.0.1. The collected data were analyzed offline, proposing a new complex variable delay-embedding dynamic mode decomposition (CDE DMD) algorithm that combines complex state filtering and time embedding to extract a linear approximate model. While the experimental results exhibited exotic curves in phase plane and time series, the analysis results showed that the proposed algorithm extracts linear and chaotic modes contributing to the data. It is concluded that the robot dynamics can be described by the linearized model interrupted by chaotic modes. The technique successfully extracts coherent modes from limited measurements and linearizes the system dynamics. Full article

Tropical cyclone prediction is often described as chaotic and unpredictable on time scales that cross into stochastic regimes. Predictions are bounded by the depth of understanding and the limitations of the physical dynamics that govern them. Slight changes in global atmospheric and oceanic conditions may significantly alter tropical cyclone genesis regions and intensity. The purpose of this paper is to characterize the predictability of seasonal storm characteristics in the North Atlantic basin by utilizing the Largest Lyapunov Exponent and Takens’ Theorem, which is rarely used in weather or climatological analysis. This is conducted for a post-weather satellite era (1960–2022). Based on the accumulated cyclone energy (ACE) time series in the North Atlantic basin, cyclone activity can be described as predictable at certain timescales. Insight and understanding into this coupled non-linear system through an analysis of time delay, embedded dimension, and Lyapunov exponent-reconstructed phase space have provided critical information for the system’s predictability. Full article

There are few works about Neimark–Sacker bifurcating analysis on discrete dynamical systems with linear diffusion and delayed coupling under periodic/Neumann-boundary conditions. In this paper, we build up the framework for Neimark–Sacker bifurcations caused by Turing instability on high-dimensional discrete-time dynamical systems with symmetrical property in the linearized system. The fractional diffusion operator in higher-dimensional discrete dynamical systems is introduced and regular/chaotic Turing patterns are discovered by the computation of the largest Lyapunov exponents. Full article

In this study, a model-free  $P{I}^{\phi }$-sliding mode control ( $P{I}^{\phi }$-SMC) methodology is proposed to synchronize a specific class of chaotic fractional-order memristive neural network systems (FOMNNSs) with delays and input saturation. The fractional-order Lyapunov stability theory is used to design a two-level  $P{I}^{\phi }$-SMC which can effectively manage the inherent chaotic behavior of delayed FOMNNSs and achieve finite-time synchronization. At the outset, an initial sliding surface is introduced. Subsequently, a robust  $P{I}^{\phi }$-sliding surface is designed as a second sliding surface, based on proportional–integral (PI) rules. The finite-time asymptotic stability of both surfaces is demonstrated. The final step involves the design of a dynamic-free control law that is robust against system uncertainties, input saturations, and delays. The independence of control rules from the functions of the system is accomplished through the application of the norm-boundedness property inherent in chaotic system states. The soft actor-critic (SAC) algorithm based deep Q-Learning is utilized to optimally adjust the coefficients embedded in the two-level  $P{I}^{\phi }$-SMC controller’s structure. By maximizing a reward signal, the optimal policy is found by the deep neural network of the SAC agent. This approach ensures that the sliding motion meets the reachability condition within a finite time. The validity of the proposed protocol is subsequently demonstrated through extensive simulation results and two numerical examples. Full article

Islanding occurs when a load is energized solely by local generators and can result in frequency and voltage instability, changes in current, and poor power quality. Poor power quality can interrupt industrial operations, damage sensitive electrical equipment, and induce outages upon the resynchronization of the island with the grid. This study proposes an islanding detection method employing a Duffing oscillator to analyze voltage fluctuations at the point of common coupling (PCC) under a high-noise environment. Unlike existing methods, which overlook the noise effect, this paper mitigates noise impact on islanding detection. Power system noise in PCC measurements arises from switching transients, harmonics, grounding issues, voltage sags and swells, electromagnetic interference, and power quality issues that affect islanding detection. Transient events like lightning-induced traveling waves to the PCC can also introduce noise levels exceeding the voltage amplitude by more than seven times, thus disturbing conventional detection techniques. The noise interferes with measurements and increases the nondetection zone (NDZ), causing failed or delayed islanding detection. The Duffing oscillator nonlinear dynamics enable detection capabilities at a high noise level. The proposed method is designed to detect the PCC voltage fluctuations based on the IEEE standard 1547 through the Duffing oscillator. For the voltages beyond the threshold, the Duffing oscillator phase trajectory changes from periodic to chaotic mode and sends an islanded operation command to the inverter. The proposed islanding detection method distinguishes switching transients and faults from an islanded operation. Experimental validation of the method is conducted using a 3.6 kW PV setup. Full article