Chaos Solitons & Fractals最新文献

{"title":"Soliton solutions with stability, bifurcation analysis and phase portraits of Kudryashov–Sinelshchikov equation","authors":"Subodh Barik, Sidheswar Behera","doi":"10.1016/j.chaos.2025.117367","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117367","url":null,"abstract":"This paper investigates the Kudryashov–Sinelshchikov equation, which describes nonlinear pressure wave propagation in liquid-gas bubble mixtures while incorporating the effects of viscosity and heat transfer. By employing a suitable traveling-wave transformation, the governing partial differential equation is reduced to an ordinary differential equation and analyzed within the approach of dynamical systems. The resulting singular system is regularized through an appropriate transformation of the independent variable, which preserves its first integral and enables detailed phase-portrait analysis. The qualitative behavior of the system is further explored using phase-plane diagrams and bifurcation analysis to identify critical transitions in wave dynamics. To construct explicit analytical solutions, the Hirota bilinear method is applied, leading to exact one-soliton, two-soliton, and three-soliton solutions. These solutions are graphically demonstrated through two-dimensional surface plots, three-dimensional visualizations, and contour profiles, which clearly illustrate the localized, stable, and interaction-preserving characteristics of the solitons. The results emphasize not only the integrability of the Kudryashov–Sinelshchikov model but also its capability to capture intricate nonlinear wave dynamics of significant physical relevance. By combining dynamical systems analysis with exact multi-soliton solutions, this study provides deeper insights into the behavior and interactions of pressure waves in dispersive and thermoviscous environments. Such an enhanced understanding establishes a valuable theoretical approach for modeling nonlinear phenomena in liquid-gas mixtures, where viscosity and heat transfer play a central role.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"88 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261920","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":"Nonreciprocal quadrature squeezing in cavity–magnon optomechanics","authors":"Yilou Liu, Rui-Shan Zhao, Kai-Kai Zhang, Jin-Fang Li, Ren-Gang Wan, Hui Sun, Xiao-Tao Xie","doi":"10.1016/j.chaos.2025.117368","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117368","url":null,"abstract":"We investigate an intriguing scheme to realize nonreciprocal quadrature squeezing in a composite system comprising a cavity coupled to a mechanical oscillator, a degenerate parametric amplifier (DPA), and a yttrium iron garnet (YIG) sphere. Through numerical simulations, we analyze the quadrature squeezing spectrum for different coupling modes. In the case of only cavity mode, increasing the nonlinear gain of the DPA enhances not only both the amplitude of the fluctuations and the squeezing strength, but also induces frequency shifts at the normal mode frequencies. Under cavity–magnon coupling conditions, the Barnett effect is used to generate nonreciprocal quadrature squeezing spectrum. The cavity–magnon coupling induces normal mode splitting, with the spacing between the split spectral dips being linearly related to the coupling strength. The nonreciprocal quadrature squeezing properties at the two normal mode frequencies are opposite, and their nonreciprocal intensity increase with the Barnett effect. When both magnon mode and mechanical mode couplings with the cavity mode are considered, the number of squeezing dips increases to three, all exhibiting significant nonreciprocity under the Barnett effect. Our research may offer new perspectives for the development of nonreciprocal magnon devices and quantum precision measurement.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"24 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261919","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":"Characterizing the edge of chaos in echo state networks","authors":"Yufei Gao","doi":"10.1016/j.chaos.2025.117333","DOIUrl":"10.1016/j.chaos.2025.117333","url":null,"abstract":"<div><div>Chaos theory examines how simple deterministic rules can produce unpredictable yet highly structured dynamics due to their extreme sensitivity to initial conditions. In reservoir computing, and particularly in Echo State Networks (ESNs), operating at the so-called “edge of chaos” has been empirically shown to maximize memory capacity and computational richness; however, a rigorous characterization of this critical regime has remained elusive. Here, we address this gap by combining propagation-of-chaos Dynamical Mean-Field Theory (DMFT) with infinite-dimensional ergodic and multiplicative-ergodic theorems and sharp spectral-gap and minorization estimates to establish, for continuous-time ESNs, the almost-sure existence of a unique critical gain <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> at which the maximal Lyapunov exponent <span><math><mrow><mi>Λ</mi><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></math></span> crosses zero. We derive an exact one-dimensional DMFT formula <span><math><mrow><mi>Λ</mi><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow><mo>=</mo><mo>ln</mo><mi>g</mi><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><msub><mrow><mover><mrow><mi>μ</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mi>g</mi></mrow></msub></mrow></msub><mrow><mo>[</mo><mo>ln</mo><mrow><mo>|</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>]</mo></mrow></mrow></math></span>, prove that it admits a single zero, and validate <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> empirically via six independent diagnostics—spectral scaling, long-range correlations, fractal attractor dimension, phase-space geometry, invariant-measure statistics, and spatio-temporal coherence. Our results provide a theoretical foundation for edge-of-chaos ESNs, illuminating why marginally stable reservoirs yield optimal performance and laying the theoretical groundwork for integrating chaotic dynamics into modern machine learning architectures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117333"},"PeriodicalIF":5.6,"publicationDate":"2025-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227082","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":"Convergence and stability analysis of a set-valued mixed variational inequality problem via three-step iterative approximation scheme","authors":"Ishfaq Ahmad Bhat ,&nbsp;Nathiya N. ,&nbsp;Mohd Iqbal Bhat","doi":"10.1016/j.chaos.2025.117221","DOIUrl":"10.1016/j.chaos.2025.117221","url":null,"abstract":"<div><div>In this paper, we introduce and investigate a novel class of set-valued mixed variational inequality problem and its equivalent form, a set-valued mixed variational inclusion problem and discuss their existence and uniqueness of solution. Further, we propose a three-step iterative scheme for approximating the solution of set-valued non-linear mixed variational inequality problem. Furthermore, we delve into the convergence and stability analysis of the proposed three-step iterative scheme. The results can be considered as a refinement of the earlier results in this domain.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117221"},"PeriodicalIF":5.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217634","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":"The symbolic partition with generalized Koopman analysis","authors":"Haipeng Li ,&nbsp;Pengfei Guo ,&nbsp;Yueheng Lan","doi":"10.1016/j.chaos.2025.117309","DOIUrl":"10.1016/j.chaos.2025.117309","url":null,"abstract":"<div><div>Symbolic dynamics serves the study of chaotic systems as a crucial tool, prompting extensive research on a proper partition of the phase space. However, the majority of prevailing methods are empirical and based either on construction of manifolds or on specific orbits. A spectral consideration based on evolution operators, such as the Koopman operator, remains underexplored. Here, we propose an alternative method for the symbolic partition based on the Koopman operator, the left eigenfunctions of which turn out closely related to the stretching and folding mechanism of chaos generation and thus provide novel means to identify a partition boundary. To avoid wild oscillations in eigenfunctions, a generalized Koopman analysis is developed to enable a local spectral computation for refining a partition. This new framework is successfully demonstrated in several typical dynamical systems including 1-D chaotic maps, the well-known Hénon maps with different parameters and a 3-D hyperchaotic map as well as a periodically driven Duffing system, with or without small noisy perturbation. Thus, the proposed technique is highly flexible and good for chaotic systems in multi-dimensions with diverse complexities.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117309"},"PeriodicalIF":5.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217636","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":"Spatial public goods game on hypergraphs with particle swarm intelligence","authors":"Shun Gao ,&nbsp;Liming Zhang ,&nbsp;Qionglin Dai ,&nbsp;Haihong Li ,&nbsp;Claudio J. Tessone ,&nbsp;Junzhong Yang","doi":"10.1016/j.chaos.2025.117304","DOIUrl":"10.1016/j.chaos.2025.117304","url":null,"abstract":"<div><div>Particle swarm optimization (PSO) has emerged as a powerful tool in evolutionary game theory, particularly for enhancing cooperation in spatial public goods games (PGGs). While existing research often focuses on one-on-one pairwise interactions, the role of PSO in fostering cooperation under many-body interactions on hypergraphs remains unexplored. Here, we extend spatial PGGs to uniform random hypergraphs (URHs) with tunable group sizes and integrate the PSO algorithm into evolutionary dynamics for agents to adapt their strategies. We consider two scenarios for the PSO, one in which cognitive component and social learning are interdependent, and the other where they are independent. We find that in the former case, PSO can promote cooperation over a larger parameter range compared to the Fermi strategy updating rule. Moreover, larger groups are more effective in promoting cooperation on URHs, enabling the population to reach a high level of cooperation. Notably, combining smaller self-cognitive adjustments with larger social influences can significantly enhance cooperation. Furthermore, in the independent case where the constraint between individual and social learning weights is relaxed, cooperation could be optimized with environment-dependent parameter settings. In particular, individual learning buffers cooperators in harsh environments, while social learning accelerates cooperation in favorable conditions. Our research underscores the effectiveness of PSO in addressing social dilemmas and advances the understanding of the interaction between individual learning and social learning in complex networked systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117304"},"PeriodicalIF":5.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217635","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":"Impact of carrying capacity on the dynamics of a discrete-time plant-herbivore system","authors":"Asifa Tassaddiq ,&nbsp;Arshad Mehmood ,&nbsp;Rizwan Ahmed","doi":"10.1016/j.chaos.2025.117284","DOIUrl":"10.1016/j.chaos.2025.117284","url":null,"abstract":"<div><div>This paper investigates the complex dynamics of a discrete-time plant-herbivore model obtained by extending an existing framework through the incorporation of a logistic growth term for the plant population, reflecting resource limitation such as nutrients, space, and light. The addition of carrying capacity introduces intraspecific competition among plants, significantly enriching the system’s behavior. We conduct a rigorous mathematical analysis to establish the existence and local stability of all biologically feasible fixed points. In particular, boundedness of solutions is proved, and in the case of saddle points, stable and unstable manifolds are explicitly computed. These results clarify the conditions under which plant and herbivore populations can persist or collapse. We further establish the occurrence of a transcritical bifurcation at the boundary equilibrium. Using bifurcation theory, we demonstrate that the system experiences both period-doubling and Neimark–Sacker bifurcations at the positive fixed point. Notably, our analysis reveals that the inclusion of logistic growth leads to a cascade of period-doubling bifurcations, ultimately resulting in chaotic dynamics, a phenomenon not reported in the original model. From a biological perspective, this suggests that resource limitation can induce irregular population fluctuations, making long-term prediction of species abundances difficult. Numerical simulations, including bifurcation diagrams, phase portraits, and Lyapunov exponent computations, are presented to support the theoretical results. This study highlights the critical role of resource limitation in ecological modeling and demonstrates how simple biologically realistic modifications can produce complex, unpredictable dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117284"},"PeriodicalIF":5.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217987","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":"Concentration and cavitation for the modified Chaplygin two-phase flow model at the vanishing pressure limit","authors":"Chun Shen ,&nbsp;Meina Sun ,&nbsp;Zhijian Wei","doi":"10.1016/j.chaos.2025.117343","DOIUrl":"10.1016/j.chaos.2025.117343","url":null,"abstract":"<div><div>Creation of delta shock and vacuum in Riemann solutions under the pressureless circumstance is derived from the corresponding ones from the modified Chaplygin flow model in the content of liquid-gas two-phase flow by sending the two perturbed parameters go to zero in the pressure simultaneously. The associated concentration and cavitation effects can be carefully observed and analyzed at such limiting procedure. It should be stressed that there exist three possible occurring scenarios about the vacuum formation by taking into account the virtual velocity within vacuum region due to the different convergence rates of the two perturbed parameters.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117343"},"PeriodicalIF":5.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217880","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":"Travelling pulses in the Barkley model: A geometric singular perturbation approach","authors":"Gabriele Grifò, Annalisa Iuorio","doi":"10.1016/j.chaos.2025.117307","DOIUrl":"https://doi.org/10.1016/j.chaos.2025.117307","url":null,"abstract":"In this work, we investigate travelling pulse solutions to the Barkley model, a prototypical example of excitable system with activator-inhibitor dynamics. Such patterns are numerically observed for a wide range of parameter values and show how coherent structures can be induced by mechanisms different from diffusion-driven instability. The intrinsic multiscale nature of this system allows us to apply Geometric Singular Perturbation Theory (GSPT) to constructively establish the existence of travelling pulses as homoclinic orbits in the corresponding three-dimensional phase-space. The analytical findings are corroborated by a thorough numerical investigation via direct simulation as well as continuation based on the software AUTO.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"8 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145229050","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":"Time fractional evolution of two superconducting charge qubits","authors":"Abdessamie Chhieb ,&nbsp;Mansoura Oumennana ,&nbsp;Mostafa Mansour","doi":"10.1016/j.chaos.2025.117331","DOIUrl":"10.1016/j.chaos.2025.117331","url":null,"abstract":"<div><div>We investigate the quantum correlation dynamics between two superconducting charge qubits (TSC-Q), governed by the time-fractional Schrödinger equation (TFSE), a framework incorporating non-Markovian memory effects arising from environmental interactions. By analyzing separable and partially entangled initial states, we highlight the central role of the fractional order <span><math><mi>τ</mi></math></span>, Josephson energies (<span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>J</mi><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>J</mi><mn>2</mn></mrow></msub></math></span>), and coupling strength (<span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>) in modulating concurrence, quantum steering asymmetry, and Bell nonlocality (via the CHSH inequality). Our results indicate that a decrease in the value of <span><math><mi>τ</mi></math></span> promotes a faster generation of quantum correlations for separable and partially entangled states, highlighting the dual role of <span><math><mi>τ</mi></math></span> as both a catalyst and a stabilizer of quantum resources. Furthermore, it is important to note that optimal behavior of quantum correlations is observed when the Josephson energies of the two qubits are close, i.e., when <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>J</mi><mn>2</mn></mrow></msub><mo>≈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>J</mi><mn>1</mn></mrow></msub></mrow></math></span>. In addition, a stronger coupling strength, denoted by <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, further enhances the generation of these correlations. The synergy among <span><math><mi>τ</mi></math></span>, <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>J</mi><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>J</mi><mn>2</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> defines a tunable parameter space for engineering memory-driven correlations to mitigate decoherence. These results position the TFSE as a promising tool for modeling non-Markovian dynamics in superconducting architectures, paving the way for robust quantum platforms with enhanced correlations, suitable for scalable quantum computing and secure communication systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117331"},"PeriodicalIF":5.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217637","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}