Chaos Solitons & Fractals最新文献

Public goods cooperation via group interaction with opponent selection 通过群体互动和对手选择进行公共产品合作

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-16 DOI: 10.1016/j.chaos.2025.116821

Ju Han , Bin Pi , Xiaojie Chen , Attila Szolnoki

{"title":"Public goods cooperation via group interaction with opponent selection","authors":"Ju Han , Bin Pi , Xiaojie Chen , Attila Szolnoki","doi":"10.1016/j.chaos.2025.116821","DOIUrl":"10.1016/j.chaos.2025.116821","url":null,"abstract":"<div><div>Understanding how cooperation emerges in biological or social systems remains a significant scientific conundrum. The public goods game is one of the most frequently used paradigms for studying the evolution of cooperative behavior in structured populations. Here we consider the group interaction with opponent selection and assume that individuals randomly choose some neighbors from the whole neighborhood to form an interaction group both in infinite and finite structured populations. Using the pair-approximation approach in the weak selection regime, we first derive the dynamical equations of the frequency of cooperators in infinitely large populations. We consider four different strategy update rules, including death-birth, imitation, birth-death, and pairwise comparison. Our findings demonstrate that death-birth and imitation updating can promote the emergence of cooperation, whereas cooperation fails to emerge under birth-death and pairwise comparison. We then extend our theoretical analysis to finite populations and respectively calculate the fixation probabilities of cooperation and defection. We identify the mathematical condition under which selection favors cooperators over defectors. Our results indicate that cooperators dominate the population more often than defectors under death-birth and imitation updating, while birth-death and pairwise comparison confer an evolutionary advantage to defection. To complete our study, the theoretical predictions are confirmed numerically and by Monte-Carlo simulations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116821"},"PeriodicalIF":5.3,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632810","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}

引用次数: 0

A dynamic information flow control framework for hyperchaos in complex-variable systems and FPGA-based applications 复杂变量系统超混沌动态信息流控制框架及fpga应用

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116858

Xiangguang Sun, Jun Zheng

{"title":"A dynamic information flow control framework for hyperchaos in complex-variable systems and FPGA-based applications","authors":"Xiangguang Sun, Jun Zheng","doi":"10.1016/j.chaos.2025.116858","DOIUrl":"10.1016/j.chaos.2025.116858","url":null,"abstract":"<div><div>Traditional chaotic systems suffer from dynamical degradation and fragile chaos caused by the fixed data flow direction in cryptographic applications. To address these limitations, this paper proposes a dynamic information flow control (DIFC) framework by introducing three novel operators to enable real-time control of information flow paths in complex-variable chaotic systems. The resulting DIFC-based complex-variable chaotic system (DIFC-CVCS) exhibits strong hyperchaotic behavior with strictly bounded trajectories and remains stable under 16-bit precision. The DIFC system achieves a near-ideal permutation entropy of average value 0.9992 and demonstrates robust chaotic properties. A pseudorandom number generator (PRNG) constructed from DIFC-CVCS passes all 15 NIST SP800-22 statistical tests with a 100% success rate. Hardware implementation on field-programmable gate arrays (FPGA) validates the practical feasibility of the design, achieving a throughput of 500 Mbps. The proposed control framework provides a new paradigm for designing high-performance and precision-resilient chaotic systems for secure applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116858"},"PeriodicalIF":5.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632809","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}

引用次数: 0

Efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators 利用齐次微分器高效可靠地重建动态吸引子

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116798

Uros Sutulovic, Daniele Proverbio, Rami Katz, Giulia Giordano

{"title":"Efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators","authors":"Uros Sutulovic, Daniele Proverbio, Rami Katz, Giulia Giordano","doi":"10.1016/j.chaos.2025.116798","DOIUrl":"10.1016/j.chaos.2025.116798","url":null,"abstract":"<div><div>Reconstructing the attractors of complex nonlinear dynamical systems from available measurements is key to analyse and predict their time evolution. Existing attractor reconstruction methods typically rely on topological embedding and may produce poor reconstructions, which differ significantly from the actual attractor, because measurements are corrupted by noise and often available only for some of the state variables and/or their combinations, and the time series are often relatively short. Here, we propose the use of Homogeneous Differentiators (HD) to effectively de-noise measurements and more faithfully reconstruct attractors of nonlinear systems. Homogeneous Differentiators are supported by rigorous theoretical guarantees about their de-noising capabilities, and their results can be fruitfully combined with time-delay embedding, differential embedding and functional observability. We apply our proposed HD-based methodology to simulated dynamical models of increasing complexity, from the Lorenz system to the Hindmarsh–Rose model and the Epileptor model for neural dynamics, as well as to empirical data of EEG recordings. In the presence of corrupting noise of various types, we obtain drastically improved quality and resolution of the reconstructed attractors, as well as significantly reduced computational time, which can be orders of magnitude lower than that of alternative methods. Our tests show the flexibility and effectiveness of Homogeneous Differentiators and suggest that they can become the tool of choice for preprocessing noisy signals and reconstructing attractors of highly nonlinear dynamical systems from both theoretical models and real data.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116798"},"PeriodicalIF":5.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632553","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}

引用次数: 0

A transformation of mappings preserving the property of robust chaos 一个保持鲁棒混沌性质的映射变换

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116827

Marcin Lawnik , Eric Campos-Cantón , Lazaros Moysis , Murilo S. Baptista , Christos Volos

{"title":"A transformation of mappings preserving the property of robust chaos","authors":"Marcin Lawnik , Eric Campos-Cantón , Lazaros Moysis , Murilo S. Baptista , Christos Volos","doi":"10.1016/j.chaos.2025.116827","DOIUrl":"10.1016/j.chaos.2025.116827","url":null,"abstract":"<div><div>Robust chaos is a phenomenon characterized by the continuous occurrence of chaos for the variability of control parameters. Therefore, chaotic systems with this property are highly desirable in various applications, e.g. chaos-based cryptography. One of the properties that allows the construction of maps with robust chaos is the S-unimodality property. This paper presents a new method to transform an S-unimodal map to its skew form while preserving the S-unimodal property. Thus, a new family of skew maps is defined with a new parameter <span><math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, which allows the generation of robust chaos for any value of the parameter <span><math><mi>q</mi></math></span>. In addition to the theoretical results concerning this transformation, a number of examples of new families of chaotic maps are presented using known classical chaotic systems, such as the logistic map or the sine map. The application of skew maps in chaotic cryptography is also discussed in this paper.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116827"},"PeriodicalIF":5.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632552","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}

引用次数: 0

Nonlinear coherent structures in two-component inhomogeneous nonlinear Schrödinger systems with inter-core coupling and four-wave mixing terms 具有核间耦合和四波混频项的双分量非均匀非线性Schrödinger系统的非线性相干结构

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116802

Emmanuel Kengne , WuMing Liu

{"title":"Nonlinear coherent structures in two-component inhomogeneous nonlinear Schrödinger systems with inter-core coupling and four-wave mixing terms","authors":"Emmanuel Kengne , WuMing Liu","doi":"10.1016/j.chaos.2025.116802","DOIUrl":"10.1016/j.chaos.2025.116802","url":null,"abstract":"<div><div>We consider a two-component nonlinear Schrödinger system with cross-phase modulation, self-phase modulation, linear-coupling nonlinearities, four-wave mixing nonlinearities, and parabolic refractive index (external potential) which governs the dynamics of nonlinear waves in anisotropic graded index nonlinear dispersive media. Performing a modified lens-type transformation and identifying an appropriate similarity transformation, the integrability conditions are presented, and the model system is converted into two independent scalar nonlinear Schrödinger equations. Depending on the sign of the inter-core coupling, our physical model behaves either like a system without dissipation having “positive coherent coupling” or like a dissipative model “negative coherent coupling” in which the inter-core coupling plays the role of dissipation. We show that the linear superposition of various nonlinear wave solutions of the derived scalar nonlinear Schrödinger equations results in several kinds of nonlinear coherent structures. Those nonlinear coherent structures show the interaction of various nonlinear waves (interaction of two bright solitons, interaction of one periodic and one aperiodic breather, interaction of two aperiodic breathers, …) and the coexistence of various kinds of nonlinear waves such as, for example, coexisting rogue wave and breather, rogue wave and rogue wave, periodic breather and aperiodic breather. Focusing on kink-like and periodically modulated nonlinearity coefficients, we show how the nonlinearities affect nonlinear coherent structures in the physical model under consideration.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116802"},"PeriodicalIF":5.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632550","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}

引用次数: 0

Predefined-time with time-varying coefficients neurodynamic for composite optimization problems 复合优化问题的时变系数预定义时间神经动力学

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116792

Dongmei Yu , Shaowei Lin , Gehao Zhang , Hongrui Yin

引用次数: 0

Dynamic Mandelbulb fractals: A mathematical framework for time-evolving 3D fractals using distance estimation 动态曼德尔布勒分形：使用距离估计的时间演变的三维分形的数学框架

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116829

Anurag Kumar, L. Bhaskar

{"title":"Dynamic Mandelbulb fractals: A mathematical framework for time-evolving 3D fractals using distance estimation","authors":"Anurag Kumar, L. Bhaskar","doi":"10.1016/j.chaos.2025.116829","DOIUrl":"10.1016/j.chaos.2025.116829","url":null,"abstract":"<div><div>This paper presents a novel approach to generating a time-dependent Mandelbulb fractal by introducing dynamic spatial transformations within its iterative construction process. By embedding smoothly varying sinusoidal translations-scaled by both global time and iteration index and synchronizing a phase-driven rotation in the XY-plane with Greenwich Mean Time, the fractal’s internal geometry undergoes continuous, organic deformation while preserving its core self-similar patterns. Leveraging a distance-estimator based raymarching pipeline in GLSL, our implementation renders these evolving structures in real time, allowing detailed exploration of their richly evolving forms.</div><div>The dynamic behavior introduced by in-loop time modulation enhances the fractal’s complexity and offers new opportunities for applications. Specifically, the time-dependent Mandelbulb provides an intuitive tool for scientific visualization, mirroring the transient structures of turbulent flows, plasma instabilities, and other chaotic systems. It also lends itself to chaos-based cryptography: by encoding secret keys into time-varying translation amplitudes, rotation phases, or exponent values, one can generate non-repeating, sensitive pseudo-random sequences for secure communication. This work not only advances real-time fractal visualization but also lays the groundwork for future exploration in dynamic simulations and fractal-driven security systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116829"},"PeriodicalIF":5.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632548","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}

引用次数: 0

Improved fixed-time sliding mode synchronization control of a new 4-cell memristive CNN chaotic system with the offset boosting via certain self-parameters 一种新型4单元记忆CNN混沌系统的改进定时滑模同步控制

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-15 DOI: 10.1016/j.chaos.2025.116800

Yuman Zhang , Yuxia Li

{"title":"Improved fixed-time sliding mode synchronization control of a new 4-cell memristive CNN chaotic system with the offset boosting via certain self-parameters","authors":"Yuman Zhang , Yuxia Li","doi":"10.1016/j.chaos.2025.116800","DOIUrl":"10.1016/j.chaos.2025.116800","url":null,"abstract":"<div><div>A new 4-cell memristive cellular neural network (CNN) is proposed, in which a current-controlled generic memristor substitutes the resistor in one cell’s output. Within the CNN system, various dynamic behaviors are generated, including symmetrical and asymmetrical double-wing chaotic attractors, single-wing chaotic attractors, and periodic attractors, resulting from bifurcation phenomena with two memristor parameters varying. More interestingly, the remaining two memristor parameters pose partially amplitude control and offset boosting to the variables or dynamics of the CNN system, due to no bifurcation phenomena by varying them. The theoretical findings are validated by circuit realization. Moreover, an improved sliding mode synchronization control for the proposed CNN system with external disturbance and non-modeled dynamics is introduced. Under the sliding mode control, the responsive system in the secure communication can achieve synchronization with the driving system, both of which are specified by the proposed CNN system. The synchronization time is fixed and independent of their initial conditions. The synchronization control strategy is robust in a degree, as the synchronization is achieved and the synchronization times are nearly indistinguishable for CNNs both with and without disturbances and non-modeled dynamics, while solving the problem of chattering. Moreover, the synchronization time can be shorten by parameters of the sliding mode surface and the controller, as well as the parameter of the additional term through decreasing the overshoot of the convergence process of the synchronization error system. Finally, all the performances are validated by numerical simulations. The research findings pave a way for future applications to secure communications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116800"},"PeriodicalIF":5.3,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632551","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}

引用次数: 0

Conformable fractional-order fixed-point state estimator for discrete-time nonlinear systems 离散非线性系统的可调分数阶不动点状态估计

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-14 DOI: 10.1016/j.chaos.2025.116825

Lorenz Josue Oliva-Gonzalez, Rafael Martínez-Guerra

引用次数: 0

Nonlinear design of tuned inertia damper: From analytical calculation to chaotic behavior prediction 调谐惯性阻尼器的非线性设计：从解析计算到混沌行为预测

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-14 DOI: 10.1016/j.chaos.2025.116854

Jialin Si , Jiaquan Xie

{"title":"Nonlinear design of tuned inertia damper: From analytical calculation to chaotic behavior prediction","authors":"Jialin Si , Jiaquan Xie","doi":"10.1016/j.chaos.2025.116854","DOIUrl":"10.1016/j.chaos.2025.116854","url":null,"abstract":"<div><div>In this study, a tuning method based on a bi-objective optimization approach—focusing on displacement and kinetic energy—is proposed for the design of Tuned Inertia Dampers (TIDs) for coupled linear and nonlinear primary systems. For the nonlinear primary system, the design criteria for the TID parameters are established through an analytical method, and the analytical expression for the steady-state frequency response of the nonlinear system is derived using the harmonic balance method (HB). A dimensional reduction analysis of the two-degree-of-freedom system is conducted, and the chaotic threshold is calculated by applying Melnikov function theory. The suppression effect of the TID parameters on the system's chaotic behavior is further verified through numerical simulations of the safety basin. Building upon this, a tuning strategy is developed with the goal of optimizing the balance between the peak displacement and kinetic energy responses of the primary system. The dynamic correlation between the optimal stiffness of the TID, the nonlinear stiffness coefficient of the primary system, and the inertia element is also explored. This method offers a design framework that combines both analytical accuracy and engineering applicability for nonlinear vibration control, particularly for structural systems with viscoelastic materials or large deformation characteristics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116854"},"PeriodicalIF":5.3,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632547","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}

引用次数: 0