Chaos Solitons & Fractals最新文献

{"title":"Generalized synchronization between two distinct chaotic systems through deep reinforcement learning","authors":"Haoxin Cheng ,&nbsp;Haihong Li ,&nbsp;Jinfeng Liang ,&nbsp;Qionglin Dai ,&nbsp;Junzhong Yang","doi":"10.1016/j.chaos.2025.116727","DOIUrl":"10.1016/j.chaos.2025.116727","url":null,"abstract":"<div><div>This study presents a novel model-free deep reinforcement learning (DRL) approach to control generalized chaotic synchronization between two distinct chaotic systems, referred to as the slave and master systems. Our method enables an agent to progressively optimize its strategy for applying external compensation to the slave system through continuous interaction with both systems, achieving generalized synchronization without requiring prior knowledge of the underlying chaotic dynamics. We validate our approach on several classical chaotic systems, including the Lorenz system, the Rössler system, and the Chua circuit, demonstrating rapid synchronization and exceptional performance. A key contribution of this work is the ability of a single learned agent to control generalized chaotic synchronization across various slave–master system configurations. The DRL approach shows remarkable robustness, maintaining effective synchronization control even with limited information about the state variables of both systems. Notably, our method successfully controls high-dimensional coupled chaotic systems while requiring only minimal state variable information. The results underscore the potential of DRL for applications in secure communication and other fields where chaos control is crucial.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116727"},"PeriodicalIF":5.3,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513648","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":"Lie symmetries, stability, and chaotic dynamics of solitons in nematic liquid crystals with stochastic perturbation","authors":"Ahmed H. Arnous","doi":"10.1016/j.chaos.2025.116730","DOIUrl":"10.1016/j.chaos.2025.116730","url":null,"abstract":"<div><div>This paper investigates the nonlinear and stochastic dynamics of solitons in nematic liquid crystals under the influence of multiplicative noise. Starting with a coupled nonlinear Schrödinger system and a reorientational equation, we apply a gauge transformation to remove stochastic perturbations modeled by Stratonovich calculus. Lie symmetry analysis is then employed to systematically reduce the resulting deterministic partial differential equations into ordinary differential equations. The dynamical system derived from the traveling-wave reduction is analyzed through phase portraits and Hamiltonian formulations, revealing various equilibrium structures. The presence of chaotic dynamics is confirmed by computing the Lyapunov exponent and visualizing phase transitions. We also derive explicit solitary and periodic wave solutions using elliptic and hyperbolic function representations. Our results demonstrate how Lie symmetries, combined with stochastic modeling, offer a powerful framework to understand and classify the complex behaviors of solitonic waves in nonlinear optical media.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116730"},"PeriodicalIF":5.3,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513651","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":"Stochastic dynamics and probability analysis for a generalized epidemic model with environmental noise","authors":"Brahim Boukanjime ,&nbsp;Mohamed Maama","doi":"10.1016/j.chaos.2025.116744","DOIUrl":"10.1016/j.chaos.2025.116744","url":null,"abstract":"<div><div>In this paper we consider a stochastic SEIQR (Susceptible–Exposed–Infected–Quarantined–Recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global positive solution to the model, ensuring that it remains well-defined over time. We further establish V-geometric ergodicity, which guarantees the exponential convergence of the system’s probability distribution to its stationary measure, providing a quantitative measure of the system’s stability over time. By leveraging Young’s and Chebyshev’s inequalities, we demonstrate the concepts of stochastic ultimate boundedness and stochastic permanence, providing insights into the long-term behavior of the epidemic dynamics under random perturbations. Additionally, we derive conditions for stochastic extinction, which describes scenarios where the epidemic may eventually die out. Finally, we perform numerical simulations to verify our theoretical results and assess the model’s behavior under different parameters.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116744"},"PeriodicalIF":5.3,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513650","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":"Coupling static opinions with evolutionary games: Shaping cooperation in spatial social dilemmas","authors":"Lijuan Qin ,&nbsp;Yali Zhang ,&nbsp;Chunpeng Du ,&nbsp;Xiaofang Duan ,&nbsp;Yikang Lu","doi":"10.1016/j.chaos.2025.116763","DOIUrl":"10.1016/j.chaos.2025.116763","url":null,"abstract":"<div><div>A fundamental feature of most game-theoretic models coupling opinions is that individuals’ opinions can change during interactions. However, this study explores the impact of static opinions on the evolution of cooperation in the spatial Prisoner’s Dilemma Game (PDG). By coupling fixed opinions with strategy interactions on a square lattice, we examine how opinion benefits, the conformity parameter, and group dominance affect cooperative behavior. Simulation results show that higher opinion benefits significantly enhance cooperation by facilitating the formation of cooperator clusters. In addition, the conformity parameter <span><math><mi>α</mi></math></span> balances the effects of opinions and strategies. Notably, balanced initial opinion distributions promote stable cooperation, whereas polarized distributions suppress it. These findings highlight the critical role of static opinions in shaping cooperative behavior and offer new insights into the mechanisms of cooperation in structured populations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116763"},"PeriodicalIF":5.3,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513653","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":"Integrability and complex dynamics of solitons of a generalized perturbed KdV equation with time-dependent variable coefficients and Coriolis effect","authors":"Dalal. M. AlMutairi ,&nbsp;M.M. Alqarni ,&nbsp;M.A. Aljohani ,&nbsp;Khadijah M. Abualnaja ,&nbsp;Emad E. Mahmoud ,&nbsp;Shabir Ahmad","doi":"10.1016/j.chaos.2025.116726","DOIUrl":"10.1016/j.chaos.2025.116726","url":null,"abstract":"<div><div>In this work, the generalized perturbed KdV equation is studied with time-dependent coefficients. The integrability of the proposed equation is demonstrated with the help of Painlevé test (<span><math><mi>P</mi></math></span>-test) criteria. It is verified that the considered equation possess analytical solutions in the form of solitons as it does not have movable singularity, which is verified via <span><math><mi>P</mi></math></span>-test. The N-soliton with time dependent coefficients is achieved via Hirota direct method. First, second and third-order soliton solutions are derived with suitable auxiliary functions. Moreover, hybrid lump solutions are attained via Hirota bilinear form. Detailed graphical presentations, including 3D visualizations, illustrate the dynamics of the soliton solutions, emphasizing the influence of the time-dependent Coriolis effect on soliton behavior. These results advance the understanding of the time-dependent integrable systems and offer significant insights into the dynamics affected by variable external factors, contributing to broader applications in fluid dynamics and nonlinear wave propagation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116726"},"PeriodicalIF":5.3,"publicationDate":"2025-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513647","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":"Multifractal analysis of thermal infrared of siltstone under uniaxial compression","authors":"Qingbin Guo ,&nbsp;Peng Liang ,&nbsp;Qun Li ,&nbsp;Shuai Wang","doi":"10.1016/j.chaos.2025.116790","DOIUrl":"10.1016/j.chaos.2025.116790","url":null,"abstract":"<div><div>Engineering practices indicate that in geological engineering, rocks can be in a uniaxial loading state. Siltstone specimens were subjected to uniaxial compression with concurrent infrared thermal image monitoring. Multifractal theory was applied, utilizing the multifractal spectrum and its parameters as quantitative indices for characterizing the infrared field's evolution during failure. On this basis, the multifractal spectrum curvature coefficient was defined to describe the infrared field characteristics. Finally, the evolution relationship between the curvature coefficient and load was investigated, advancing from qualitative to quantitative assessment. The results show that: The multifractal spectrum of infrared thermal image of siltstone has left hook shape and bell shape. The evolution process of multifractal spectrum is closely related to the loading process of siltstone, the pre-peak stage is left hook-shaped, the post-peak stage evolves from left hook-shaped to bell-shaped, and when it fracture, it mutates into left hook-shaped. The evolution trends of multifractal parameters <span><math><mi>Δ</mi><mi>α</mi></math></span> and <span><math><mi>Δ</mi><mi>f</mi><mfenced><mi>α</mi></mfenced></math></span> are similar, they change steadily in the pre-peak stage, increase continuously in the post-peak stage, and suddenly drop to the initial level when fracture occurs. The curvature coefficient of the multifractal spectrum exhibits a slow decrease before the peak, followed by a rapid decrease to a range of 2 to 4 after the peak, and a sudden increase to its initial level upon fracture, with an initial value of approximately 7.5. Through qualitative and quantitative analysis of the correlation between the curvature coefficient and load at the same moment, it was found that during the pre-peak stage, the correlation is predominantly negative, with the area of the negatively correlated envelope being 4.9 times larger than that of the positively correlated envelope. In the post-peak stage, the correlation is predominantly positive, with the area of the positively correlated envelope being 11.7 times larger than the negatively correlated area. This demonstrates that the curvature coefficient can effectively characterize the evolution of load during the loading process of siltstone. The research results provide a new method for the quantitative analysis of thermal infrared fields during the rock failure process, offering new insights for the early warning of engineering rock mass catastrophes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116790"},"PeriodicalIF":5.3,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501520","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":"Species vulnerability and ecosystem fragility: A dual perspective in food webs","authors":"Emanuele Calò ,&nbsp;Giordano De Marzo ,&nbsp;Vito D.P. Servedio","doi":"10.1016/j.chaos.2025.116741","DOIUrl":"10.1016/j.chaos.2025.116741","url":null,"abstract":"<div><div>Ecosystems face intensifying threats from climate change, overexploitation, and other human pressures, emphasizing the urgent need to identify keystone species and vulnerable ones. While established network-based measures often rely on a single metric to quantify a species’ relevance, they overlook how organisms can be both carbon providers and consumers, thus playing a dual role in food webs. Here, we introduce a novel approach that assigns each species two complementary scores—an importance index quantifying their centrality as carbon source and a predatory index capturing their vulnerability. We show that species with high importance index are more likely to trigger co-extinctions upon removal, while high-robustness index species typically endure until later stages of collapse, in line with their broader prey ranges. On the other hand, low robustness index species are the most vulnerable and susceptible to extinctions. Tested on multiple food webs, our method outperforms traditional degree-based analyses and competes effectively with eigenvector-based approaches, while also providing additional insights. This scalable and data-driven approach, relying solely on interaction data, provides a cost-effective tool that complements expert classifications for prioritizing conservation efforts.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116741"},"PeriodicalIF":5.3,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501517","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":"A new kind of global solution for the MHD boundary layer system","authors":"Huashui Zhan","doi":"10.1016/j.chaos.2025.116753","DOIUrl":"10.1016/j.chaos.2025.116753","url":null,"abstract":"<div><div>The MHD boundary layer describes the behavior of electrically conducting fluids (such as plasmas or liquid metals) in the presence of a magnetic field. By the Crocco inverse transformation, the MHD boundary layer system is transformed to a parabolic equation, which is called as the MHD boundary layer equation. Under the Oleinik assumption, the existence of the local analytic solution can be proved similar to the Prandtl boundary layer system. In order to overcome the difficulties arising from the degeneracy and the singularity of the MHD boundary layer equation, we used some innovative variable substitutions and introduce two new kinds of BV entropy solutions. By choosing a suitable test function, we were surprised to discover that the stability of entropy solutions can be proved independent of the boundary value condition. This novel finding provides a fresh perspective for re-examining relevant issues in the future, particularly regarding the potential significance of nonlinear boundary conditions historically imposed on MHD boundary layer equations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116753"},"PeriodicalIF":5.3,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144511061","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":"Left-definite fractional Hamiltonian systems: Titchmarsh-Weyl theory","authors":"Ekin Uğurlu","doi":"10.1016/j.chaos.2025.116756","DOIUrl":"10.1016/j.chaos.2025.116756","url":null,"abstract":"<div><div>Hamiltonian systems are useful when formally symmetric boundary value problems generated by ordinary derivatives are considered. However, if the ordinary derivatives are changed by non-integer-order (fractional) derivatives, it is not easy to investigate the corresponding problems. In this paper, we introduce a systematic approach to dealing with fractional boundary value problems by constructing a fractional Hamiltonian system. In particular, we consider a left-definite system, and we construct nested-circles theory (Weyl theory) for this system of equations. Using the Titchmarsh-Weyl function, we prove that at least <span><math><mi>r</mi></math></span>-solutions of the <span><math><mrow><mn>2</mn><mi>r</mi></mrow></math></span>-dimensional system of equations should be Dirichlet-integrable on a given interval.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116756"},"PeriodicalIF":5.3,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144511062","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":"Cooperation dilemmas in multi-stage public goods games with finite populations","authors":"Yewei Tao ,&nbsp;Xiaoqian Zhao ,&nbsp;Wenhua Li ,&nbsp;Kaipeng Hu ,&nbsp;Lei Shi","doi":"10.1016/j.chaos.2025.116714","DOIUrl":"10.1016/j.chaos.2025.116714","url":null,"abstract":"<div><div>Cooperation in the real world is often based on continuous inputs in multiple stages, and the realization of cooperative outcomes depends on individual strategic choices in multiple successive stages. However, this mechanism of stage benefit accumulation and delayed distribution may compress the viability of cooperation and exacerbate the evolutionary pressure faced by cooperators. In this paper, we construct a two-stage public goods game model based on finite populations, and examine the effects of different selection intensities and stage synergy factors on the evolution of the system. It is found that under the setting of cumulative gains and delayed allocation, it is difficult for cooperators to resist the joint exploitation by defectors at different stages, and the system is more inclined to evolution to a mixed-strategy pattern dominated by first-stage cooperation only. It is difficult to change the cooperation disadvantage by enhancing the first-stage synergies alone, and it is also difficult to realize the full cooperation steady state by enhancing the two-stage synergy factors at the same time. In contrast, weak selection or smaller group sizes can help alleviate the pressure of strategic exploitation and provide a narrow space for cooperation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116714"},"PeriodicalIF":5.3,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501519","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}