Chaos Solitons & Fractals最新文献

{"title":"Evolution and regulation of transverse cross-modulated cosine-Gaussian beams in a three-region configuration","authors":"Zhuoyue Sun ,&nbsp;Jie Li ,&nbsp;Zhiping Dai ,&nbsp;Duo Deng ,&nbsp;Zhaoguang Pang ,&nbsp;Zhenjun Yang","doi":"10.1016/j.chaos.2026.118132","DOIUrl":"10.1016/j.chaos.2026.118132","url":null,"abstract":"<div><div>The evolution and regulation of transverse cross-modulated cosine-Gaussian beams in a three-region configuration composed of free space, left-handed materials (LHMs), and gradient-index (GRIN) media are investigated. The analytical expressions of beam transmission, beam width and its change rate, beam width extreme, phase wavefront curvature and its change rate, and phase wavefront curvature extreme are derived. The effects of the transverse cross modulation parameter, the refractive index of LHMs and the distribution coefficient of GRIN media on the beam evolution are investigated. By adjusting the refractive index in the LHMs, the transmission process in the LHMs can be realized as the inverse transmission process in the free space. Moreover, under appropriate parameter conditions, the three-region configuration allows the beams to exhibit soliton-like behavior. The study in this paper can provide a reference for the mode control of practical optical systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118132"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279146","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":"An improved Q-learning algorithm integrating past and future rewards","authors":"Qiu Lou,&nbsp;Dun Han,&nbsp;Mei Sun","doi":"10.1016/j.chaos.2026.118127","DOIUrl":"10.1016/j.chaos.2026.118127","url":null,"abstract":"<div><div>Achieving stable and efficient learning remains a core challenge in reinforcement learning. However, traditional <span><math><mi>Q</mi></math></span>-learning methods often suffer from instability and slow convergence due to an unbalanced focus on either immediate or future rewards, while neglecting the role of past rewards. To address this, we propose an improved <span><math><mi>Q</mi></math></span>-learning algorithm that systematically integrates both past and future rewards through a balancing factor. Specifically, we design three reward weighting strategies: static discount, double exponential discount, and weighted moving average, to process past rewards. Theoretical analysis proves the convergence of the algorithm and reveals that the weighted moving average method minimizes reward variance. In a series of simulation experiments, we find that the weighted moving average approach significantly outperforms other methods in terms of convergence speed, cumulative reward, and learning stability. This study provides a new perspective on reward utilization in reinforcement learning through the balancing factor and adaptive weighting mechanisms.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118127"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147330273","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":"Supersonic solitary waves in non-local bistable lattices","authors":"P.Q. Li,&nbsp;K.F. Wang,&nbsp;B.L. Wang","doi":"10.1016/j.chaos.2026.118139","DOIUrl":"10.1016/j.chaos.2026.118139","url":null,"abstract":"<div><div>Non-local interactions are receiving increasing attention in the control of wave propagation in metamaterials. Nevertheless, the role of non-local interactions in shaping solitary wave profiles, admissible supersonic regimes, stability, and instability-induced evolution remains largely unexplored. To address these challenges, supersonic solitary waves in bistable lattices are studied through a combined theoretical and numerical approach, revealing how non-local effects govern their wave dynamics. We first demonstrate that non-locality serves as an effective tool for tuning wave morphology: positive stiffness coupling leads to wave broadening, whereas negative stiffness coupling enhances localization. More importantly, we reveal that strong negative stiffness interactions fundamentally alter the dispersion relation, thereby redefining the supersonic regimes where supersonic solitary waves exist. Furthermore, it is found that weak negative stiffness non-locality can enhance the stability of solitary waves, standing in sharp contrast to other non-local interactions that tend to shrink the stable domain. When stability is lost, two distinct evolution pathways are identified: one involves a nonlinear self-adjustment toward a stable high-speed attractor, and the other entails a fission process that generates multiple coherent structures, including transmitted/reflected waves and pinned breathing waves. Finally, during boundary interactions, non-local effects are crucial both for maintaining wave integrity and for potentially mediating the conversion between solitary and transitional waves. These findings provide a robust theoretical foundation for designing advanced mechanical metamaterials with programmable wave characteristics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118139"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147330301","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":"Influential node identification via network embedding and structural feature fusion","authors":"Heping Zhang ,&nbsp;Li Dong ,&nbsp;Weida Xu ,&nbsp;Yang Wu ,&nbsp;Xiaoyi Jin ,&nbsp;Xiaoyao Xie ,&nbsp;Hegui Zhang","doi":"10.1016/j.chaos.2026.118092","DOIUrl":"10.1016/j.chaos.2026.118092","url":null,"abstract":"<div><div>Influential node identification in complex networks remains challenging due to limited generalizability and high computational costs of existing methods. To address these issues, we reformulate the task as a regression problem and propose CNINI (Complex Network Influential Node Identification), a framework that integrates network embedding with local centrality measures to capture both global topological structures and local influence patterns. CNINI employs network embedding techniques to learn node representations, which are combined with centrality measures to construct more informative features. In a supervised setting, the SIR model is used to simulate influence propagation and generate training labels. The regression model is trained on multiple synthetic networks and then applied to unseen networks, reducing the need for costly iterative propagation simulations during inference. Extensive experiments on eight real-world datasets demonstrate that CNINI surpasses 11 state-of-the-art baseline methods, including centrality- and embedding-based methods.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118092"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778550","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":"Exact solution for the three-state asymmetric Potts model on a Cayley tree","authors":"Farrukh Mukhamedov ,&nbsp;Hasan Akın","doi":"10.1016/j.chaos.2026.118118","DOIUrl":"10.1016/j.chaos.2026.118118","url":null,"abstract":"<div><div>In this study, we investigate the Gibbs measures of an asymmetric Potts model on a Cayley tree with asymmetric branching couplings (<span><math><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≠</mo><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>), revealing new critical phenomena and phase transitions that extend beyond the classical, symmetric case. The Gibbs distributions are derived based on the Kolmogorov consistency condition, and the recursive equations governing the system are formulated. We analyze the solutions of these recurrence relations by identifying their fixed points and exploring their behavior under specific symmetry assumptions. We analyze the extremality conditions of the disordered phases corresponding to translation-invariant Gibbs measures using the eigenvalues of the stochastic matrices constructed using the tree-indexed Markov chain approach. Furthermore, we compute the free energy of the model as a function of the compatible boundary conditions (CBC) and derive the associated thermodynamic quantities through its derivatives. The convexity properties of the system are examined in the configuration space <span><math><msup><mrow><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msup></math></span>, providing further insights into the structure of the Gibbs measures. Finally, to study the dynamical features of the model — such as chaoticity, periodicity, and bifurcations — we calculate the Lyapunov exponent, offering a deeper understanding of the system’s complex behavior. Furthermore, the dynamical evolution toward the thermodynamic limit is characterized through a 2D stability analysis based on the Oseledets theorem. By employing trajectory embedding, we identify global basin restructuring at the phase transition thresholds and confirm the structural stability of the model, rigorously proving the absence of chaotic attractors within the physical parameter space.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118118"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777675","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":"Unveiling cooperative dynamics in scale-free networks through adaptive deep Q-networks","authors":"Zhipeng Yang ,&nbsp;Xianjia Wang ,&nbsp;Yanling Li ,&nbsp;Zhenghui Liu ,&nbsp;Ran Li ,&nbsp;Wanli Yue","doi":"10.1016/j.chaos.2026.118149","DOIUrl":"10.1016/j.chaos.2026.118149","url":null,"abstract":"<div><div>Understanding how cooperation emerges and persists in social dilemmas remains a central focus of scientific inquiry. Previous studies have shown that highly heterogeneous network structures can significantly promote cooperative behavior. To advance this understanding, we investigate the evolution of cooperation in Prisoner’s Dilemma games on scale-free networks and propose a novel strategy update framework: the Adaptive Exploration Deep Q-network Strategy Update method (ADQSU). ADQSU integrates an adaptive exploration mechanism that enables agents to dynamically modulate their exploration probability based on historical payoffs, while employing a Deep Q-Network (DQN) to effectively incorporate past experiences and environmental signals for policy optimization. Additionally, a diversified payoff mechanism is introduced to link individual behavioral states with local social relationships, thereby incentivizing collaborative strategies. Simulation results demonstrate that ADQSU, combined with a neighbor-state-weighted payoff scheme, outperforms traditional update rules in fostering widespread cooperation. Further analysis reveals that increasing the average degree of the network enhances cooperative behavior, with highly connected nodes acting as central propagators of cooperation. These findings not only deepen our understanding of cooperative dynamics in complex networks but also provide actionable insights for the design of cooperation-enhancing mechanisms in decentralized systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118149"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279145","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":"Intrinsic noise reveals the stability of a neuronal network","authors":"Marcelo Bussotti Reyes ,&nbsp;Ramon Huerta ,&nbsp;Pedro Valadão Carelli ,&nbsp;Reynaldo D. Pinto ,&nbsp;Mikhail I. Rabinovich ,&nbsp;Allen I. Selverston","doi":"10.1016/j.chaos.2026.118083","DOIUrl":"10.1016/j.chaos.2026.118083","url":null,"abstract":"<div><div>The stability of rhythmic activity in neural networks is an important aspect in the study of central pattern generators (CPGs). Different from other physiological rhythms, the activity of CPGs has not been fully characterized in terms of its stability, especially using quantitative methods. We propose a method that takes advantage of the natural noise present in CPGs to quantify the stability of the rhythmic activity. Furthermore, we used the stationary bootstrap method to define confidence intervals of the results. We applied this method to study the influence of a synaptic modification on the pyloric CPG circuit, using artificial synapses implemented in dynamic clamp software. We show that even after removing one of its strongest synapses, the CPG stability remains unaltered. This analysis suggests that CPGs are designed to be strongly stable regardless of the parameter perturbations they undergo.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118083"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329772","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":"Dynamics analysis of a two-degree-of-freedom fractional-order maglev system under slotting effect and time-delay control","authors":"Wan-qi Sun ,&nbsp;Mei-qi Wang ,&nbsp;Peng-fei Liu ,&nbsp;Rui-chen Wang ,&nbsp;Xin Liang","doi":"10.1016/j.chaos.2026.118085","DOIUrl":"10.1016/j.chaos.2026.118085","url":null,"abstract":"<div><div>To improve the operational stability of high-speed maglev trains under complex multi-source excitations, this study aims to clarify the nonlinear dynamic mechanisms induced by controller time delay, slotting disturbance, and suspension-guidance coupling-phenomena that remain insufficiently understood in existing research. A two-degree-of-freedom maglev model is established incorporating suspension–guidance coupling and the fractional viscoelasticity of air springs. A time-delay PD controller is introduced, and the slotting effect is modeled as a harmonic track excitation. The primary resonance response is derived using the multi-scale and harmonic balance methods, and the stability conditions are obtained via Lyapunov's first method and the Routh-Hurwitz criterion. A systematic parametric investigation is conducted to evaluate how time delay, structural nonlinearity, fractional order, and control gains modulate the amplitude-frequency characteristics, stability boundaries, and bifurcation evolution. Time-domain simulations further reveal the transitions among periodic, quasiperiodic, and chaotic responses. The results show that these parameters jointly reshape the resonance peak, shift the instability region, and generate closed frequency islands and multistable behaviors. Time delay is identified as the dominant factor that amplifies nonlinear effects and induces chaotic instability. Increasing the delay leads to frequent alternations between periodic and chaotic states as system parameters vary, highlighting the heightened complexity of the maglev system's dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118085"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329773","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":"Chaotic polarization dynamics of dissipative vector solitons in mode-locked fiber lasers","authors":"Qiuying Ma ,&nbsp;Haoyang Yu ,&nbsp;Minghui Niu ,&nbsp;Wenjie Feng ,&nbsp;Defeng Zou ,&nbsp;Youjian Song","doi":"10.1016/j.chaos.2026.118125","DOIUrl":"10.1016/j.chaos.2026.118125","url":null,"abstract":"<div><div>Chaotic dissipative solitons have attracted increasing attention in recent years as paradigmatic objects for exploring nonequilibrium nonlinear dynamics with direct relevance to a wide range of physical systems. However, this progress has been largely confined to scalar frameworks. In comparison, how chaos emerges and evolves in dissipative soliton systems endowed with additional internal degrees of freedom remains largely unexplored. Here we address this problem in vector solitons of a mode-locked fiber laser numerically, where orthogonally polarized field components are intrinsically coupled. We show that the route to chaos is not universal but strongly conditioned by the polarization state. For polarization-locked vector solitons, chaotic behavior predominantly manifests in the intensity dynamics, while the polarization remains constrained by nonlinear phase locking. In contrast, polarization-rotating vector solitons undergo a clear period-bifurcation route to chaos, during which the polarization states evolve from a fixed point to discrete multi-period trajectories and eventually delocalize over the Poincaré sphere, indicating simultaneous chaos in both intensity and polarization. These results highlight polarization dynamics as a key ingredient in dissipative soliton physics and reveal chaotic regimes that emerge only from polarization-resolved dynamics, extending the landscape of dissipative soliton dynamics beyond scalar soliton models.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118125"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329812","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":"Recent advances and challenges of manipulation of micro- and nanoparticles by surface acoustic wave in microfluidics","authors":"Wenbo Han ,&nbsp;Zhihang Fu ,&nbsp;Zhiwei Xu ,&nbsp;Hongyuan Zou ,&nbsp;Haoyu Yue ,&nbsp;Wei Li ,&nbsp;Hongpeng Zhang","doi":"10.1016/j.chaos.2026.118063","DOIUrl":"10.1016/j.chaos.2026.118063","url":null,"abstract":"<div><div>As an efficient mechanical wave technology, surface acoustic wave (SAW) has shown significant potential in the field of particle manipulation in microfluidic systems in recent years. This paper systematically reviews the recent advances, key mechanisms, application fields and future challenges of SAW-driven microfluidic particle manipulation. SAW excites surface mechanical waves through a piezoelectric substrate to form a periodic pressure gradient in the microfluidic channel, and uses acoustic radiation force, viscous resistance and inertial effect to control particle motion. It has the advantages of high resolution, fast response and low power consumption. Compared with traditional manipulation technologies (such as microporous filtration and electrophoresis manipulation), SAW technology can accurately separate particles of different sizes, morphologies and densities. In recent years, the efficiency of SAW manipulation has been significantly improved by optimizing the frequency, amplitude and microfluidic channel design of acoustic waves. In terms of application, SAW technology has been successfully used in circulating tumor cell (CTCs) manipulation, rapid detection of pathogens, synthesis of nanoparticles and monitoring of water pollutants. By summarizing the mechanism and application of SAW particle manipulation, this paper provides theoretical and technical references for the high-precision, high-throughput and multifunctional development of microfluidic technology.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118063"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329819","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}