Search Results (693)

Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration of three biologically realistic features that have not previously been combined: (i) fractional-order memory effects via a Caputo derivative of order $\alpha \in (0,1]$, (ii) two distinct biological delays—an infection transmission delay ${\tau }_1$ and a predator handling delay ${\tau }_2$—and (iii) nonlocal spatial dispersal modeled through fractional Laplacian operators ${(-\Delta )}^{\gamma /2}$. This triple integration enables the model to capture long-range temporal memory, delayed biological responses, and nonlocal spatial interactions simultaneously, offering insights into dynamics that are challenging to capture with classical integer-order or single-delay formulations. The fractional Laplacian generalizes classical diffusion by allowing long-range dispersal events (Lévy flights), where individuals can occasionally move over large distances with heavy-tailed step-size distributions—a phenomenon observed in many animal movement patterns but absent from standard diffusion models. We provide rigorous proofs of solution existence, uniqueness, non-negativity, and boundedness in both temporal and spatiotemporal settings. Local asymptotic stability conditions are derived for all feasible equilibrium states via characteristic equation analysis. The coexistence equilibrium undergoes a Hopf bifurcation when either delay crosses a critical threshold, with fractional order $\alpha$ modulating the bifurcation point and post-bifurcation oscillation frequency. A Lyapunov functional demonstrates global asymptotic stability of the infection-free equilibrium under biologically interpretable conditions. Turing instability analysis reveals conditions for spontaneous pattern formation, with the fractional exponent $\gamma$ controlling pattern wavelength and correlation length. Numerical simulations validate theoretical predictions, including spatial patterns, traveling waves, and chaos. To bridge theory with potential applications, we outline a statistical framework for parameter estimation and uncertainty quantification, suggesting that $\beta$, $\alpha$, and ${\tau }_1$ may be priority targets for parameter estimation. Full article

In this study, we analyze the solution characteristics and dynamics of a variable-order fractional (V-OF) Arneodo system using the Liouville–Caputo fractional operator with variable order. The V-OF operator is used to describe the time-dependent memory effect in the system, which leads to more complex and diverse dynamics compared to integer-order systems. In this work, numerical simulations are performed to observe the effect of the order functions on the dynamic behaviors of the system. In addition, the phase portraits, time series graphs, and three-dimensional diagrams are used to analyze the dynamic behaviors and different types of oscillations present in the system. Furthermore, the bifurcations, chaotic behaviors, and stability of the system with variable orders are studied, and it is found that the system has more complex dynamics compared to the integer-order case. In this case, the Lyapunov exponents indicate that the system under investigation is sensitive to the initial conditions, and the memory effect can control the chaotic oscillation depending on the order of the functions. Full article

The goal of laser polishing (LP) is to improve the surface quality of functional parts, components, and assemblies. LP is a complex nonlinear thermophysical process, in which laser radiation induces localized melting of a material with an initially rough surface topography. During LP, the thermodynamic state evolves dynamically due to transient melt flow, heat transfer, and rapid solidification within the laser–material interaction zone. A smooth surface is formed through the interplay between surface tension-driven flow, which promotes energy minimization, and nonequilibrium effects associated with melting and solidification. From the perspective of self-organization, LP can be interpreted as an open system driven by energy input, where complex material redistribution leads to the evolution of surface topography. In this work, the self-organization of molten material is analyzed using chaos-based descriptors, including the Lyapunov exponent, phase portrait, approximate entropy, and the Hurst exponent, calculated from measured surface topographies before and after laser polishing. The results show that LP acts as a spatial low-pass filter, reducing high-frequency surface components associated with micromilling marks, and exhibits a directional bias in material redistribution relative to the laser scanning direction. Among the evaluated descriptors, the Lyapunov and Hurst exponents demonstrate consistent behaviors, indicating their suitability as robust indicators of surface state in post-process analysis. For the investigated conditions (Inconel 718), a laser fluence of 158.3 mJ/cm² provided the best-achieved surface quality, corresponding to an improvement in surface roughness (Ra) of approximately 70% and the lowest Lyapunov exponent of 1.966 and highest Hurst exponent of 0.859. This study demonstrates that chaos-based analysis of surface topography provides a phenomenological framework for assessing process stability and surface evolution, offering a basis for thermophysics-informed development of LP in applications such as mold and die manufacturing. Full article

Chaotic itinerancy—irregular switching among metastable collective states—provides a dynamical substrate for flexible social coordination, yet its mechanistic origin in multi-agent systems remains unclear. We present a multi-agent Active Inference model in which chaotic itinerancy emerges from Expected Free Energy minimisation without outcome-level social priors. Agents select actions to minimise Expected Free Energy while updating preferences through a precision-gated learning mechanism modulated by interpersonal trust. Hill-function nonlinearity in state transitions creates bistable “affordance landscapes” that gate behavioural mode switching. Simulations with small number of agents on an Erdos–Rényi trust network reveal spontaneous alternation among multiple metastable behavioural clusters, heavy-tailed dwell-time distributions, and sign-changing finite-time Lyapunov exponents—three hallmarks of chaotic itinerancy. Crucially, replacing Hill-function dynamics with linear transitions reduces the chaotic-itinerancy detection rate from 80% to 20%, demonstrating that nonlinear affordance structure is necessary for generating metastable switching. We further show that agents with simplified internal models of the world sustain richer itinerant dynamics as a group than “perfect-foresight” agents, suggesting that bounded rationality may be functionally advantageous for maintaining behavioural flexibility. These results establish active inference as a principled framework for modelling chaotic itinerancy in social systems and offer a computational account of trust-mediated collective transitions observed in theatre workshops and group dynamics. Full article

We study the long-time behavior of nonlinear stochastic evolution equations in a separable Hilbert space driven by a Q-Wiener process. The linear part of the equation is generated by a strongly continuous semigroup with an exponential dichotomy, which provides fixed rates of decay and growth. The nonlinear drift and diffusion terms are globally Lipschitz and become small as time tends to infinity. Our main result shows that under these conditions, the mean-square Lyapunov exponents of the nonlinear system coincide with those of the linear part. In other words, nonlinear stochastic perturbations that decay in time do not change the main growth or decay rates of solutions in the mean-square sense. This result provides simple and verifiable criteria ensuring that the long-time Lyapunov behavior of the nonlinear stochastic equation is fully determined by the linear semigroup, even in the presence of time-dependent stochastic perturbations. Full article

This study proposes a novel image encryption algorithm based on a two-dimensional discrete chaotic system that integrates cellular automata (CA) with a tent map. The algorithm addresses security vulnerabilities in digital image transmission and storage across open networks or cloud environments. It employs a three-phase encryption process: coordinate permutation, spatial permutation, and diffusion. Sequential application of Arnold’s coordinate scrambling, maze traversal-based spatial rearrangement, and a CA-driven diffusion mechanism enhances robustness against noise, differential attacks, and partial cropping. A Dynamic CA–Tent Map (DCA–TM) hybrid chaotic system is designed to overcome periodicity and limited key space issues inherent in conventional chaotic encryption. The permutation stage is refined into coordinate and spatial phases to achieve comprehensive pixel randomization. During diffusion, CA rules are selected dynamically based on the iteration counts of the initial parameters, yielding an adaptive encryption system with a variable key space. Performance evaluations—including Lyapunov exponent tests, bifurcation analysis, information entropy measurement, and pixel correlation assessment—confirm the strong chaotic behavior and high security of the proposed scheme. Full article

This paper introduces a rigorous class of two-dimensional Markov-switching autoregressive moving-average (2D MS-ARMA) models for spatial lattice data exhibiting regime-dependent dynamics. The switching mechanism is governed by a latent causal Markov random field that drives spatial transitions between regime-specific autoregressive and moving-average structures. We provide sufficient conditions for the existence of a strictly stationary solution through the top Lyapunov exponent associated with a sequence of random matrices obtained from a state-space representation constructed along the lexicographic order. For the first-order bidirectional specification, we derive explicit spectral conditions linking stationarity to the regime-dependent spectral radii. Sufficient conditions ensuring the existence of finite second-order moments are also provided. Parameter estimation is carried out using a variational expectation–maximization (VEM) algorithm based on a mean-field approximation of the posterior distribution of the hidden regimes. The E-step yields closed-form coordinate ascent updates, while the M-step relies on gradient-based numerical optimization with derivatives computed via recursive differentiation. Under increasing-domain asymptotics, we discuss the consistency and asymptotic behavior of the variational estimator. The proposed framework fills a methodological gap between classical one-dimensional Markov-switching ARMA models and spatial autoregressive structures by extending regime-switching theory to multi-indexed processes with rigorous probabilistic foundations. It provides a comprehensive basis for statistical inference, model diagnostics, and prediction in spatially heterogeneous environments. Full article

Nonlinear analysis provides a framework for understanding the complexity and stability of human locomotion by capturing dynamic patterns beyond linear methods. This study examined the effect of data length on seven nonlinear measures: Sample Entropy (SpEn), Approximate Entropy (ApEn), Lyapunov Exponents using Wolf’s (LyE_W) and Rosenstein’s (LyE_R) algorithms, Detrended Fluctuation Analysis (DFA), Correlation Dimension (CD), and the Hurst–Kolmogorov process (HK). A 3500-frame kinematic dataset from a healthy adult performing motor-assisted elliptical training and treadmill walking was segmented from 100 to 3500 frames in 10-frame increments. Data from treadmill and elliptical conditions were analyzed and presented in a combined manner to highlight general stabilization trends across locomotor tasks. Results revealed that increasing data length significantly affected all nonlinear metrics (p ≤ 0.0005). Stabilization occurred at varying minimum lengths: SpEn at ~4.5–8.8 s (540–1060 frames), ApEn at ~5.4–7.7 s (650–920 frames), LyE_W at ~19.1–29.2 s (2290–3500 frames), LyE_R at ~1.3–1.5 s (150–180 frames), DFA at ~29.2 s (3500 frames), CD at ~1.7–15.9 s (200–1910 frames), and HK at ~9.1–9.8 s (1090–1180 frames). Notably, HK achieved stable estimates in approximately one-third of the time required for DFA and substantially less than LyE_W, supporting its suitability for time-constrained or clinical settings. These findings suggest the need to tailor data collection to each nonlinear metric and to report data length explicitly to improve accuracy, reproducibility, and methodological rigor in gait variability research. However, these findings should be interpreted within the limitations of a single-participant, exploratory design. Full article

In this paper, a supply–demand–price network model incorporating a marginal feedback mechanism is proposed to characterize the evolution of market prices. Unlike classical supply–demand models, the marginal effect of excess demand, defined as the rate of change in excess demand, is explicitly introduced into the price adjustment process. As the coefficient of the marginal feedback term varies, the system exhibits rich and complex nonlinear dynamics. In particular, the model gives rise to a centrally symmetric double-wing chaotic attractor, as well as a pair of coexisting single-wing chaotic attractors. The transition routes among different dynamical regimes are systematically analyzed using phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, multistability phenomena are observed, including the coexistence of equilibrium points, limit cycles, and chaotic attractors. The corresponding basins of attraction are illustrated to reveal their intricate and interwoven structures. In addition, the emergence of endogenous chaos is investigated through both theoretical analysis and numerical simulations. Finally, the consistency between the model dynamics and real market data provides empirical evidence supporting the validity and applicability of the proposed framework. Full article

Chaotic behavior in power systems that are integrated with permanent-magnet synchronous generators (PMSGs) poses a significant threat to stability and security. Existing control methods often suffer from slow convergence, reliance on precise system models, or the inability to guarantee convergence within a predefined time. To address these issues, this paper develops a predefined-time synchronization control scheme for chaotic PMSG systems under unknown nonlinearities and external disturbances. First, an adaptive neural network with variable exponent coefficients is constructed to approximate unknown system dynamics online. Second, a predefined-time stability criterion is established, ensuring global convergence of synchronization errors within a user-specified time, independently of initial conditions. Third, the proposed controller achieves superior disturbance rejection without requiring prior knowledge of disturbance bounds. Numerical simulations demonstrate that the proposed method outperforms conventional finite-time control in convergence speed, control smoothness, and robustness to parameter variations—offering a practical and theoretically guaranteed solution for enhancing the stability of PMSG-based power systems. Full article

In this paper, we study the dynamical analysis and solutions of the fractional Benjamin–Bona–Mahony–Burger equation. We demonstrate various derived solutions using different definitions of fractional derivatives, namely the $\beta$-derivative, conformable derivative, and M-truncated derivative, to examine their kinetic characteristics. Firstly, we find the solution of the fractional Benjamin–Bona–Mahony–Burger equation using two different approaches. We then discuss the effects of the fractional derivative on the solutions using 3D graphical discussion. Finally, we discuss the dynamical analysis using sensitivity and chaos analysis. We also discuss the chaos analysis using permutation entropy, 2D and 3D phase portrait, fractal dimension, time analysis, return map, Lyapunov exponent, and multistability through Poincare map and basins of attraction. To explore a diverse range of phenomena across the fields of physical science and engineering, this study highlights the computational strength and flexibility of the proposed method. Full article

Impulsive noise significantly degrades the performance of power line communication (PLC) systems due to their non-Gaussian amplitude distribution, burst clustering, and inherent temporal dependence. Conventional statistical and spectral models often describe marginal behavior but do not fully account for the underlying temporal organization of such noise processes. This paper introduces an ensemble-based non-linear dynamical framework for the short-window characterization of impulsive PLC noise using delay-embedded phase-space reconstruction (PSR). Rather than relying on extended stationary recordings, the analysis is conducted across multiple independent short-duration acquisition windows obtained from indoor low-voltage networks. For each realization, the delay parameter is selected using average mutual information, and the embedding dimension is determined through the false nearest neighbors (FNN) criterion. The reconstructed trajectories are then examined using correlation dimension estimation, largest Lyapunov exponent analysis, and recurrence quantification measures. The resulting non-linear descriptors reveal structured phase-space organization and low-dimensional dynamical characteristics that are not readily observable in the original time-domain representation. In addition, these findings show that short-window PLC data preserve meaningful dynamical characteristics and support the use of non-linear geometric descriptors for impulsive PLC noise analysis and future mitigation approaches. Full article

This paper proposes a novel four-dimensional strongly dissipative nonlinearly coupled hyperchaotic system, investigates its dynamical characteristics, and demonstrates its applicability through Deoxyribonucleic Acid (DNA)-encoded RGB image encryption. First, a four-dimensional nonlinearly coupled hyperchaotic system with strong dissipativity is constructed. Nonlinear dynamics analysis methods, including phase trajectory diagrams, Lyapunov exponent spectra, and bifurcation diagrams, are employed to thoroughly reveal the system’s complex dynamical evolution mechanisms. The analysis indicates that the system not only possesses a wide range of chaotic parameters but also exhibits rich phenomena of multiple coexisting attractors, demonstrating a high degree of multistability. This characteristic offers potential advantages for image encryption, as it increases the diversity of dynamical behaviors and enhances sensitivity to initial conditions. The physical realizability of the chaotic behavior is further verified through an analog circuit implementation. Consequently, the system supports the design of encryption algorithms with larger key spaces, stronger resistance to phase space reconstruction, and improved pseudo-randomness, making it particularly suitable for applications with extremely high security requirements. Subsequently, leveraging the highly random chaotic sequences generated by this system, combined with various DNA coding rules and operations, the RGB image components are scrambled and diffused for encryption. Security analysis demonstrates that the algorithm effectively passes examinations across multiple dimensions, including histogram analysis, information entropy, adjacent pixel correlation, Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI), and The Peak Signal-to-noise Ratio (PSNR). It achieves favorable encryption results, significantly enhances image resistance against attacks, and provides a reliable technical solution for the secure transmission of remote sensing and military images. Full article

Age-related changes in walking are often evaluated using performance-based measures, but little is known about how trunk-derived gait quality changes across healthy adulthood during habitual walking. This study examined gait quality using a single inertial measurement unit positioned at the lower back to record acceleration and angular velocity signals during approximately 5 min of continuous self-selected overground habitual walking in healthy adults across multiple age groups spanning adulthood. Step and stride symmetry were derived from trunk acceleration autocorrelation, local dynamic stability was quantified using the maximum Lyapunov exponent, and smoothness was derived from trunk angular velocity. Associations with age were evaluated, and additional analyses examined whether hip muscle strength and physical activity contributed to inter-individual variation in these gait measures. Age was associated with lower step symmetry and reduced local dynamic stability, whereas smoothness showed more limited age-related changes. Hip extensor and internal rotator strength explained additional variance in specific gait quality measures, while physical activity showed limited associations. These findings indicate that a single lower-back IMU can detect subtle age-related differences in interpretable gait quality during habitual walking across adulthood. Full article

Because the introduction of a vibro-impact structure can widen the bandwidth and improve the harvesting efficiency of the vibration energy harvesting (VEH) systems, an analytical method for a VEH system based on vibro-impact is proposed to employ the stochastic response and stability. Firstly, the piezoelectric control equation is decoupled by the generalized harmonic transformation, which obtains an uncoupled equivalent system. Secondly, the Itô stochastic differential equation with amplitude is analytically derived by applying the proposed analytical method. Furthermore, the influence of crucial parameters on the mean square voltage (MSV) and the mean output power is explored, such as the coupling factors and restitution coefficient. Finally, the top Lyapunov exponent (TLE) can be derived based on the linearized averaged Itô equations and the condition for the stability with probability one is obtained. It turned out that restitution coefficient r and time constant ratio $\mu$ have remarkable effects on the system’s stability. Full article