Chaos Solitons & Fractals最新文献

{"title":"Research on a novel weak fault detection method based on vibrational resonance in high-dimensional chaotic system, and variational mode decomposition","authors":"Zhile Wang ,&nbsp;Xiaoli Yu ,&nbsp;Yu Guo ,&nbsp;Jianhua Yang ,&nbsp;Zijian Qiao","doi":"10.1016/j.chaos.2026.118084","DOIUrl":"10.1016/j.chaos.2026.118084","url":null,"abstract":"<div><div>This paper constructs a high-dimensional Lorenz–Stenflo model by introducing perturbation parameters based on the Lorenz–Stenflo chaotic system. The theoretical framework of vibrational resonance is established by incorporating both low-frequency and high-frequency excitation signals into the system, where the high-frequency component enhances the system response to low-frequency signal, and thus enable weak-signal detection. Specifically, the dynamical characteristics of chaotic system are modified such that the response amplitude to the low-frequency signal reaches its extremum by tuning the amplitude or frequency of high-frequency signal. The mapping relationship is derived among the response amplitude gain of low-frequency signal, high-frequency excitation parameters, and system parameters. The non-monotonic variation of this relationship with respect to these parameters indicates the occurrence of vibrational resonance in the system. In addition, the output of vibrational resonance system is susceptible to interference under strong noise conditions. To mitigate this issue, the parameterized variational mode decomposition method is employed for preprocessing, effectively suppressing strong noise. Comparative analysis across different evaluation index demonstrates that fractional multiscale phase permutation entropy is suitable for selecting the optimal modal component. Experimental results show that the proposed vibrational resonance system effectively extracts fault features of rolling bearing, thereby validating and extending the applicability of vibrational resonance theory in signal processing.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118084"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Emergent togetherness through multilayer and high-order synchronization in generative dance neuro-motor systems","authors":"Yago Emanoel Ramos ,&nbsp;Raphael Silva do Rosário ,&nbsp;Adriana de Faria Gehres ,&nbsp;Maria João Alves ,&nbsp;Ana Maria Leitão ,&nbsp;Cecília Bastos da Costa Accioly ,&nbsp;Fatima Wachowicz ,&nbsp;Ivani Lúcia Oliveira de Santana ,&nbsp;José Garcia Vivas Miranda","doi":"10.1016/j.chaos.2026.118081","DOIUrl":"10.1016/j.chaos.2026.118081","url":null,"abstract":"<div><div>Collective improvisation in dance provides a rich natural laboratory for investigating emergent coordination in coupled neuro-motor systems. Here, we examine how training shapes spontaneous synchronization patterns across movement dynamics and brain activity during collaborative performance, with particular emphasis on the structure of higher-order interactions. Using a dual-recording protocol integrating 3D motion capture and hyperscanning EEG, participants engaged in free, interaction-driven, and rule-based improvisation tasks before and after a generative dance program grounded in cellular automata principles. Motor behavior was characterized through a time-resolved α-exponent derived from Movement Element Decomposition, capturing fluctuations in energetic strategies and the exploration of degrees of freedom. Synchronization events were quantified using Motif Synchronization for biomechanical data and multilayer Time-Varying Graphs for neural data. In order to investigate collective organization beyond pairwise coupling, biomechanical synchronization networks were further analyzed using simplicial complexes, allowing the characterization of interaction structures at multiple orders, including dyads, triads, and quartets. The results reveal that training modulates the distribution of interaction orders, with pronounced effects at the pairwise level. In parallel, neural data indicate increased inter-brain synchronization following training, particularly in frontal regions, suggesting enhanced alignment of internal cognitive and intentional processes. Together, these findings suggest that togetherness in collaborative improvisation emerges as a high-order dynamical property of social systems rather than as mere motor similarity. This study highlights the nonlinear and hierarchical nature of social coordination and offers a principled framework for modeling collective behavior in creative human systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118081"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Security-conscious dynamic output feedback control for periodic piecewise nonlinear systems under output-reliant disturbance observer","authors":"Thangavel Satheesh ,&nbsp;Rathinasamy Sakthivel ,&nbsp;Oh-Min Kwon","doi":"10.1016/j.chaos.2026.118064","DOIUrl":"10.1016/j.chaos.2026.118064","url":null,"abstract":"<div><div>This article focuses on addressing the finite-time dynamic output feedback control problem for periodic piecewise nonlinear systems in the midst of multifaceted disturbances and cyber attack scenarios. Moreover, multifaceted disturbances encompass mismatched disturbances and multiple matched disturbances. Therein, the mismatched disturbances are presumed to be norm-bounded vectors, whereas multiple matched disturbances emanate from exogenous systems. Additionally, two instances of nonlinear dynamics in the plants are looked at, pertaining to both known and unknown cases. Furthermore, to estimate the multiple matched disturbances, output-reliant multiple periodic piecewise disturbance observers for both the nonlinear instances are framed separately on the grounds of the control input and the measurement output. Moreover, the mismatched disturbances are attenuated using the mixed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>/passivity approach. From thereon, a holistic control framework blending these observers with a dynamic output feedback mechanism is put together to guarantee the intended closed-loop performance in a finite-time span by rejecting the matched disturbances. Therein, a probabilistic model with Bernoulli-distributed variable is laid out to characterize the incidence of deception attacks, potentially improving the resilience of the control. Following that, by means of Lyapunov stability theory, the stability of the target system is analyzed and the precise setups of the periodic piecewise controller and disturbance observer gains are put forward. Ultimately, simulation results are put forward to confirm the reliability and effectiveness of the control protocol.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118064"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Control of the composite spiral waves: Noise can alter the structure of composite spiral waves and facilitate transitions between composite and classic spiral waves","authors":"Jian Gao,&nbsp;Bin Xu,&nbsp;Cong Liu,&nbsp;Chuansheng Shen","doi":"10.1016/j.chaos.2026.118143","DOIUrl":"10.1016/j.chaos.2026.118143","url":null,"abstract":"<div><div>Spiral waves are ubiquitous structures in a broad spectrum of natural and engineering systems, and effective control of spiral wave architectures carries both theoretical significance and potential application value. This study investigates the impact of noise on the composite spiral wave (CSW) dynamics and their structural transitions to classical spiral waves. Using a discrete spatiotemporal predator–prey reaction–diffusion model, we demonstrate that noise critically regulates the CSW structure through dual-threshold phase transitions. Numerical simulations and theoretical analyses reveal that when noise intensity exceeds critical thresholds, discontinuous first-order transitions occur: first altering the size of the small spiral wave (SSW) region, then driving global expansion into classical spiral waves. Mechanistically, noise induces local state mutations and modifies boundary propagation velocities, enabling chiral inversion of wave patterns. The system exhibits resilience, spontaneously recovering CSW structures upon noise removal. These findings establish noise as a potent tool for controlling nonlinear wave structures, with implications for cardiac arrhythmia mitigation and programmable metamaterial design.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118143"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Skewness-Kurtosis: Small samples and power-law behavior","authors":"Carlo De Michele ,&nbsp;Samuele De Bartolo","doi":"10.1016/j.chaos.2026.118066","DOIUrl":"10.1016/j.chaos.2026.118066","url":null,"abstract":"<div><div>Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail heaviness and peakedness of probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and complex systems, important aspects of their empirical behavior remain unclear — particularly in small samples and in relation to their hypothesized power-law scaling. In this work, we address both issues using a combination of empirical and synthetic data. First, we establish a lower bound for sample kurtosis as a function of sample size and skewness. In doing this, a remarkable deltoid-shaped domain appears for <span><math><mi>n</mi></math></span> = 4, which in case of discrete distributions exhibits fractal properties reflecting the underlying geometrical constraints of skewness–kurtosis space. Second, we examine the conditions under which the 4/3 power-law relationship between kurtosis and skewness emerges, effectively extending Taylor’s power-law to higher-order moments. Our results show that this scaling predominantly occurs in data sampled from heavy-tailed distributions and medium/large sample sizes, highlighting the interplay between tail behavior and sample size in shaping the empirical behavior of higher-order moments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118066"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146187552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coherent control of polarization-dependent spatio-temporal solitons in chiral quantum-dot nanostructures","authors":"Muhammad Idrees, Abeer S. Altowyan, Jabir Hakami, Xiaosen Yang, Yuee Xie, Yuanping Chen","doi":"10.1016/j.chaos.2026.118575","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118575","url":null,"abstract":"We theoretically investigate the coherent control of polarization-dependent spatio-temporal solitons in chiral quantum-dot nanostructures. The system is modeled as a four-level chiral quantum dot medium, incorporating interdot tunneling, magnetic excitation, and coherent interactions driven by optical probe and control fields, with the Hamiltonian treated under the dipole and rotating-wave approximations. Quantum interference, governed by the relative phase of the control field and the tunneling strength, enables dynamic tuning of the complex refractive index for right- and left-circularly polarized beams. Both dispersion and absorption are sensitively modulated by the chiral coupling, allowing the medium to support diverse self-sustained nonlinear excitations, including bright, dark, and periodic spatio-temporal solitons. The soliton dynamics, analyzed as functions of normalized propagation distance and time, show that enhanced tunneling reshapes soliton velocity, temporal width, and spatial confinement while preserving chiral asymmetry. These results highlight the interaction of tunneling-modified electronic states, field-induced coherence, and polarization-selective effects, demonstrating the potential of chiral quantum-dot nanostructures for polarization-controlled photonic devices and soliton-based optical information processing.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"138 1","pages":"118575"},"PeriodicalIF":7.8,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic stability of a stochastic vegetation-water model in arid ecosystems","authors":"Hongxia Zhang, Youming Lei, Zigang Li, Jun Su, Wei Xu","doi":"10.1016/j.chaos.2026.118582","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118582","url":null,"abstract":"This paper investigates the deterministic and stochastic dynamic stability of a three-variable vegetation-water ecosystem under different stochastic environmental disturbances, considering both multiplicative and additive noises. For the deterministic case, the stability of equilibria is assessed through the Jacobian matrix eigenvalues, initial state trajectories and bifurcation structure. In the stochastic case, the stability of the cube basin is analyzed using the first escape probability, derived from the Itô stochastic differential equation with six boundary conditions. Theoretical results align with Monte Carlo simulations of the original system, confirming the validity of the calculations. Findings reveal that the stability of the vegetation-free equilibrium depends on the existence of vegetation-positive equilibrium. Stochastic disturbances, especially the environmental disturbance of vegetation, enhances the stability of ecosystem. On the contrary, soil water and rainfall disturbances disrupt the stability of the system, providing insights for ecosystem protection.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"48 1","pages":"118582"},"PeriodicalIF":7.8,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive neural network passivity-based control with state observer for partially unknown nonlinear systems","authors":"Junjie Gong ,&nbsp;Shengjie Guo ,&nbsp;Jian Chen ,&nbsp;Dengsheng Cai ,&nbsp;Liang He ,&nbsp;Wei Wei ,&nbsp;Yu Long","doi":"10.1016/j.chaos.2026.117989","DOIUrl":"10.1016/j.chaos.2026.117989","url":null,"abstract":"<div><div>To overcome the limitations of interconnection and damping assignment passivity-based control (IDA-PBC) in partially unknown nonlinear systems, particularly the reliance on large damping coefficients that may cause control inputs to exceed physical constraints, this paper proposes a novel adaptive neural network passivity-based control strategy incorporating a passivity-based observer. In the proposed framework, neural networks are introduced to relax the strict requirement of the desired closed-loop port-controlled Hamiltonian (PCH) model and to construct dynamic compensation mechanisms. These mechanisms are embedded into the interconnection and damping assignment passivity-based observer (IDA-PBO), resulting in an adaptive neural network IDA-PBO (ANNIDA-PBO) with enhanced dynamic compensation capability. On the control side, neural-network-based adaptive laws and compensation terms are developed to accurately approximate and compensate for unmodeled dynamics. This design alleviates the inherent limitation of conventional IDA-PBC methods that depend on large damping coefficients to achieve robustness. As a result, the proposed framework enables a well-conditioned selection of control gains within physical constraints and effectively decouples the strong dependence between robustness performance and damping parameters in standard IDA-PBC designs. Furthermore, the closed-loop system is shown to be semi-globally uniformly ultimately bounded through port-controlled Hamiltonian modeling and Lyapunov stability analysis. Finally, simulation studies on two representative nonlinear systems are conducted to validate the proposed method, demonstrating improved control accuracy and enhanced robustness against external disturbances.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"207 ","pages":"Article 117989"},"PeriodicalIF":5.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Predicting the onset of period-doubling bifurcations via dominant eigenvalue extracted from autocorrelation","authors":"Zhiqin Ma ,&nbsp;Chunhua Zeng ,&nbsp;Ting Gao ,&nbsp;Jinqiao Duan","doi":"10.1016/j.chaos.2026.118010","DOIUrl":"10.1016/j.chaos.2026.118010","url":null,"abstract":"<div><div>Predicting the occurrence of transitions in the qualitative dynamics of many natural systems is crucial, yet it remains a challenging task. Generic early warning signals like variance and lag-1 autocorrelation identify critical slowing down near tipping points but lack practical thresholds for predicting imminent transitions. More recent studies found that the dynamical eigenvalue is rooted in the framework of empirical dynamical modeling and then estimates the dominant eigenvalue of a system from time series, providing a threshold (<span><math><mo>|</mo></math></span>DEV<span><math><mo>|</mo></math></span> = 1) to predict bifurcations and classify their types. However, its application requires careful calibration of the hyperparameters and focuses on reconstructing system dynamics directly from data. Here, we employ Ornstein–Uhlenbeck process to derive analytic approximations for the lag-<span><math><mi>τ</mi></math></span> autocorrelation function prior to period-doubling bifurcation thereby estimating the dominant eigenvalue of dynamical systems, named dominant eigenvalue extracted from autocorrelation (DE-AC), and revealing its dynamic behavior when approaching a period-doubling bifurcation. Theoretically, dominant eigenvalue tends to <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> when the system approaches a period-doubling bifurcation. In particular, we evaluated DE-AC on simulation data from cardiac alternans model and on experimental data from chick heart aggregates undergoing a period-doubling bifurcation. DE-AC reliably detected the beginning of the cardiac arrhythmia (period-doubling bifurcation) in most cases. Moreover, it demonstrated superior sensitivity and specificity as an early warning signal compared to the three widely used indicators—variance, lag-1 autocorrelation, and dynamical eigenvalue. Our theoretical and empirical results suggest that DE-AC represents a quantitative measure for predicting the onset of potentially dangerous alternating rhythms in the heart. The ability to better infer, detect, and distinguish the nature of impending transitions in complex systems will help humans manage critical transitions in biological systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"207 ","pages":"Article 118010"},"PeriodicalIF":5.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stabilization of fractional parabolic equations through designed robust Robin boundary controller","authors":"Hassen Arfaoui","doi":"10.1016/j.chaos.2026.118003","DOIUrl":"10.1016/j.chaos.2026.118003","url":null,"abstract":"<div><div>The paper deals with the boundary stabilization for time-fractional parabolic equations (TFPEs) with non-constant coefficients and distributed disturbance by backstepping approach. Firstly, boundary stabilization is investigated through right Robin boundary control (RRBC) with homogeneous left Robin boundary condition at the lower end of the spatial domain. In this context, we proved a Mittag-Leffler stability result for the solution of the TFPEs. To achieve this objective, a robust boundary feedback control law has been designed for the stabilization of the TFPEs by backstepping approach. To the best of our knowledge, the stabilization of TFPEs with left homogeneous Robin boundary condition through right Robin-type boundary feedback control law via backstepping method is novel. Some numerical examples are presented at the end of this paper to confirm the theoretical results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"207 ","pages":"Article 118003"},"PeriodicalIF":5.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}