Chaos Solitons & Fractals最新文献

{"title":"Almost periodic dynamics and stability in neutral-type BAM neural networks on time scales","authors":"Nada K. Mahdi,&nbsp;Ayad R. Khudair","doi":"10.1016/j.chaos.2026.118072","DOIUrl":"10.1016/j.chaos.2026.118072","url":null,"abstract":"<div><div>Neutral-type bidirectional associative memory (BAM) neural networks with leakage arise in applications where the present state depends on delayed rates of change together with distributed dissipation. In this paper, we study such networks on almost periodic time scales, providing a unified framework that covers both continuous- and discrete-time models.</div><div>We propose a neutral-type BAM model with distributed leakage delays and almost periodic coefficients. By defining an operator on a Banach space of almost periodic functions and proving that it is a contraction, we establish the existence and uniqueness of an almost periodic solution. Moreover, by constructing a Lyapunov functional tailored to the neutral structure and the distributed leakage terms, we obtain global exponential stability of this almost periodic solution.</div><div>The resulting criteria give explicit sufficient conditions that guarantee convergence independently of the initial history and clarify how the leakage kernels and neutral terms influence the decay rate. A numerical example in the continuous-time case illustrates the theoretical results and confirms the predicted convergence behavior.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118072"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386439","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":"Text meets topology: A dynamic graph learning method with Dy-GNNs and LLMs for tracking text attributed community evolution in complex networks","authors":"Sruthi K.S.,&nbsp;A. Sreekumar,&nbsp;Kannan Balakrishnan","doi":"10.1016/j.chaos.2026.118121","DOIUrl":"10.1016/j.chaos.2026.118121","url":null,"abstract":"<div><div>This work proposes a novel fusion framework that reformulates community evolution prediction as a temporal edge classification problem in dynamic text-attributed graphs. Our approach integrates state-of-the-art Large Language Model (LLM)-based textual embeddings with structural and temporal information, directly embedding semantic signals into the message-passing mechanisms of multiple architecturally enhanced dynamic graph neural networks (Dy-GNNs). LLMs can represent the rich text associated with node or edge attributes to generate the textual embeddings of the data. The combined textual and structural embedding of dynamic networks is then used to train deep models to predict edge classes, which is subsequently modified into community prediction. The fusion approach offers a more efficient model that can understand the evolution patterns of dynamic networks in real-world applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118121"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777176","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":"When moving away reduces polarization: Selective depolarization by endogenous migration in attraction–repulsion opinion dynamics","authors":"Hong Zhang","doi":"10.1016/j.chaos.2026.118128","DOIUrl":"10.1016/j.chaos.2026.118128","url":null,"abstract":"<div><div>Opinion polarization poses a fundamental challenge for contemporary societies, yet how spatial mobility coevolves with attraction–repulsion influence remains poorly understood. We develop an agent-based model in continuous two-dimensional space that couples tolerance-based attraction–repulsion opinion updates with endogenous migration: agents interact locally and then move toward ideologically similar neighbors while avoiding dissimilar ones. Extensive parameter sweeps show that mobility acts as a <em>selective depolarizer</em>. Above a critical tolerance threshold, mobility suppresses repulsion-driven extremization by enabling agents to leave antagonistic neighborhoods before repeated hostile encounters accumulate. At the same time, mobility strengthens spatial assortativity, yielding a robust <em>depolarized segregation</em> regime in which ideological polarization remains low while spatial clustering is high—demonstrating that echo-chamber-like structure need not coincide with ideological extremism. Across conditions, tolerance sets the dominant phase boundary, whereas exposure, interaction radius, and movement speed primarily modulate transition locations and time scales. As a mechanistic model, these results highlight a trade-off between reduced extremization and reduced cross-cutting contact, and suggest that interventions focusing only on mobility or exposure may have limited impact when tolerance is low; linking model parameters to concrete policy levers requires empirical calibration.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118128"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778114","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":"Caputo–Orlicz framework for functions of bounded Ψ-variation and exact fractal dimensions of their graphs","authors":"R.G.P. Sudha,&nbsp;R. Uthayakumar","doi":"10.1016/j.chaos.2026.118148","DOIUrl":"10.1016/j.chaos.2026.118148","url":null,"abstract":"<div><div>Fractional calculus provides a fundamental analytical framework for modeling nonlocal and memory-dependent phenomena in complex and biological systems, where classical smoothness assumptions often fail. In this paper, we develop a unified Caputo–Orlicz framework for the geometric analysis of continuous functions whose Caputo fractional derivatives possess bounded <span><math><mi>Ψ</mi></math></span>-variation, with <span><math><mi>Ψ</mi></math></span> a superlinear Young function. Using Orlicz–Hölder inequalities and Luxemburg norm techniques, we prove that the Caputo fractional derivative acts as a bounded linear operator on Orlicz variation spaces and preserves controlled modulus of continuity properties. These analytic results enable us to derive sharp bounds and exact formulas for the Hausdorff and box-counting dimensions of function graphs over both smooth and possibly fractal domains. In particular, we show that superlinear Orlicz growth enforces minimal graph dimensionality, revealing a sharp transition between smooth and fractal geometric regimes. This work establishes a rigorous connection between fractional differentiation, generalized variation theory, and fractal geometry, providing a flexible theoretical foundation for analyzing nonlinear fractional models that arise in contemporary applied mathematics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118148"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279144","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":"From Hertzian contact to Pochhammer-Chree dynamics: Solitons, chaos, and bifurcation in granular metamaterials","authors":"Mst. Ifat Zahan Soma ,&nbsp;Tarikul Islam ,&nbsp;Tobibur Rahman ,&nbsp;Shahariar Ryehan","doi":"10.1016/j.chaos.2026.118133","DOIUrl":"10.1016/j.chaos.2026.118133","url":null,"abstract":"<div><div>This study is concerned with the complex propagation patterns of solitary waves within one-dimensional metamaterials consisting of discrete granular elements. Granular mechanics relies heavily on the Hertzian contact theory, a concept which has not been adequately captured by linearised models of particulate contact. In this work, the Hertz theory of contacts is extended to the nonlinear Pochhammer-Chree equation, incorporating spatiotemporal dispersion effects. We present exact solitary wave solutions using the improved auxiliary equation and the improved tan-hyperbolic methods. These methods provide solutions which include the Kink, Anti-kink, Dipole, and Bell-shaped solitary waves, as well as compactons, which have characteristic localisation of energy. The progression of these wave patterns with differing roughness parameters is depicted through three-dimensional surface plots and contour profiles. A comprehensive bifurcation analysis has been carried out to establish the system's stability and to examine the onset of chaos, which is induced by external forcing, by applying the Melnikov theory. Analytical predictions are validated against Discrete Element Method (DEM) simulations, demonstrating excellent agreement with an Error Value (RMSE) of approximately <span><math><mn>1.2</mn><mo>%</mo></math></span>. The computed Lyapunov exponent was positive (<span><math><mn>1.9515</mn></math></span>), which suggests that the system is sensitive to initial conditions. This new approach is the most advanced that has been developed to date for calculating the nonlinear propagation of stress waves and is essential for designing materials and structures that are resistant to earthquake damage.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118133"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329816","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":"Infinite emergent oscillations with locally stable equilibrium","authors":"Ning Wang ,&nbsp;Bei Gao ,&nbsp;Haoming Zou ,&nbsp;Wentao Liu ,&nbsp;Zhixuan Ma ,&nbsp;Herbert Ho-Ching Iu ,&nbsp;Quan Xu","doi":"10.1016/j.chaos.2026.118090","DOIUrl":"10.1016/j.chaos.2026.118090","url":null,"abstract":"<div><div>The emergence of multistable states brings about significant unpredictability and complexity in nonlinear dynamical systems, which will induce undesired states and may lead to critical failures or misleading dynamics detection. In this paper, a simple five-term autonomous dissipative chaotic system with unique sine nonlinearity is presented. Notably, an infinite many coexisting attractors can emerge even if the system has a single Lyapunov and Jacobi stable equilibrium point. These attractors cannot be triggered by the initial trajectories near the small neighborhoods of the stable equilibrium point, leading to hidden extreme multistability. Bifurcation route, phase portraits, and basin of attraction confirm coexistence among different periodic and chaotic hidden oscillations. To reveal the boundary between the hidden oscillations and the locally stable space, Jacobi stability and instable boundary analysis using Kosambi–Cartan–Chern theory based on the principles of Finsler space theory are presented. Besides, a predefined-time controller is designed to stabilize the hidden oscillations, which has highlights in the independence between the initial conditions and the predefined settling time, as well as a single flexible adjusted parameter. Simulation experiments confirm the correctness of the theoretical analyses.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118090"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386378","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":"Decision complexity in co-opetitive supply chain: Innovation spillover under cartel and non-cooperative modes","authors":"Yuanyuan Zhang,&nbsp;Shaochuan Fu,&nbsp;Zihan Ma,&nbsp;Fangfang Ma","doi":"10.1016/j.chaos.2026.118055","DOIUrl":"10.1016/j.chaos.2026.118055","url":null,"abstract":"<div><div>Sourcing from competitors triggers innovation spillovers that challenge cooperative stability and strategic decisions. This study employs a nonlinear dynamic game-theoretic model to analyze supply chain behavior under two innovation modes: non-cooperative (firms independently set prices and innovation levels) and cartel cooperative (joint innovation optimization followed by independent pricing). Incorporating behavioral economics (perceived unfairness) and market heterogeneity (brand differentiation), the model reveals how strategic interactions drive system evolution. Key findings demonstrate that while high innovation spillovers enhance knowledge sharing and increase cartel profits within stable regimes, they simultaneously amplify system fragility—exceeding critical spillover thresholds induces bifurcation and chaotic dynamics, disrupting pricing mechanisms and causing severe profit volatility. Furthermore, perceived unfairness reduces cooperation willingness through negative feedback loops, destabilizing alliances, while brand differentiation exhibits dual effects: moderate levels bolster market stability whereas excessive differentiation erodes resilience. Attraction basin analysis confirms the coexistence of multi-stability states (periodic, quasi-periodic, chaotic), highlighting strategic uncertainty.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118055"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146209825","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":"Nonlinear response identification of a parametrically excited bistable magnetic rolling pendulum harvester by 0–1 test and recurrence plots","authors":"Wei Wang ,&nbsp;Zihao Yang ,&nbsp;Enna Zhang ,&nbsp;Shuangyan Liu ,&nbsp;Xiaoqing Ma ,&nbsp;Zilin Li ,&nbsp;Ronghan Wei","doi":"10.1016/j.chaos.2026.118077","DOIUrl":"10.1016/j.chaos.2026.118077","url":null,"abstract":"<div><div>Owing to the low damping characteristics, magnetic rolling pendulum gains extensive adoption in vibration energy harvesting. Bistable magnetic rolling pendulum harvester (BMRPH) exhibits chaotic and (quasi-)periodic vibrational responses, and effectively identifying the complex dynamic behaviors is essential for advancing practical applications. Therefore, this paper utilizes 0–1 test and recurrence plot (RP) to examine the nonlinear voltage response time series of a parametrically excited BMRPH. By analyzing the nonlinear dynamics of the BMRPH, multiple vibrational patterns are emphasized. Results indicate that 0–1 test could easily distinguish between chaotic and periodic responses through the trajectory plot of (<em>p</em>, <em>q</em>), total mean square displacement, and asymptotic growth rate. Unlike 0–1 test, which provides a binary classification (0 for periodic and 1 for chaotic systems), RP offers a more nuanced approach by not only distinguishing between chaotic and periodic dynamics but also revealing the relative complexity within periodic regimes. In general, the identification results align well with complementary diagnostic methods, including phase portraits, Poincaré maps, frequency spectra, and multiscale entropy, thereby offering valuable insights for optimizing the dynamic performance and enhancing energy harvesting efficiency.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118077"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777182","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":"Boundary-induced multistability and bursting oscillations in frequency switching slow–fast systems","authors":"Jiahao Zhao ,&nbsp;Xiujing Han ,&nbsp;Wenjie Zuo ,&nbsp;Jiadong Wang ,&nbsp;Meng Han","doi":"10.1016/j.chaos.2026.118080","DOIUrl":"10.1016/j.chaos.2026.118080","url":null,"abstract":"<div><div>Frequency-switching mechanisms, prevalent in engineering and scientific dynamical systems, introduce non-smooth dynamics that significantly impact system behavior. This study integrates frequency switching with slow–fast analysis in non-smooth dynamical systems, emphasizing the role of switching-induced multistability in shaping bursting dynamics. Using a modified normal-form vector field of a transcritical bifurcation subjected to state-dependent frequency-switching excitation, we show that although individual subsystems exhibit only equilibrium solutions, their interactions across the switching boundary induce non-smooth periodic orbits. These limit cycles coexist with equilibria, yielding switching-induced multistability. This multistability governs frequency-switching dynamics and determines the organization, patterns, and stability of bursting oscillations through a dual regulation mechanism involving the switching threshold and initial conditions: the switching threshold drives bifurcation evolution to control post-switching attractor selection, yielding diverse bursting patterns characterized by monostable–monostable, bistable–bistable, and bistable–monostable switching sequences; meanwhile, initial conditions exploit multistability to provide alternative stable switching pathways, thereby avoiding trajectory divergence during switching transitions and stabilizing bursting solutions. Our findings contribute to the characterizing and regulating bursting dynamics in frequency-switching systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118080"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777187","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":"Robustness of interdependent directed hypergraphs with completely connected component","authors":"Zhengao Guo ,&nbsp;Yinzuo Zhou ,&nbsp;Jie Zhou","doi":"10.1016/j.chaos.2026.118091","DOIUrl":"10.1016/j.chaos.2026.118091","url":null,"abstract":"<div><div>Directed hypergraphs (DH) provide a powerful framework for characterizing directional influences and higher-order interactions in complex systems. In many real-world systems, the group interactions represented by directed hyperedges generally have an inherent requirement of integrity, meaning their functionality depends on the simultaneous presence of all participating nodes. Traditional definition of strongly connected components that was proposed for classic directed graphs do not explicitly capture this requirement, which may lead to biased evaluation in the robustness of the system. To address this issue, we introduce the concept of the Completely Connected Component (CCC) of DH as a pertinent representation for such connectivity. By requiring that every directed hyperedge should satisfy the integrity condition, the CCC ensures the preservation of nodes incident to related hyperedges. In this paper we study the robustness of interdependent DH from the perspective of CCC, which has wide applications in many real-world systems. Based on a bipartite representation of DH, we develop a theoretical framework for analyzing the system. We systematically evaluate the system’s robustness under different types of interdependencies induced from CCC. Our analysis shows that the requirement of the integrity of hyperedges will markedly influence the robustness of the system, which is verified with numerical simulations. Specifically, since the CCC condition reinforces the preservation of nodes, interdependence between hypergraphs that takes place on nodes typically exhibit stronger robustness than that involving hyperedges. However, the system could be more vulnerable when the initial damage targets nodes rather than hyperedges. By analyzing the competing effects induced by the CCC on both the initial damage and the objects involved in the interdependence, non-monotonic behaviors of the system robustness are revealed. Our finding offers a deeper understanding of the robustness of systems with high-order interactions across various interdependence scenarios.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118091"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778549","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}