Chaos Solitons & Fractals最新文献

{"title":"Corrigendum to “Impact of system and stochastic parameters on the performance of a 3-DOF energy harvester in a two-dimensional flow field” [Chaos, Solitons Fractals 199 (2025) 116801]","authors":"Ying Hao,Jinghan Li,Zhiqiang Wu","doi":"10.1016/j.chaos.2026.119275","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119275","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"10 1","pages":"119275"},"PeriodicalIF":7.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149089928","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":"Corrigendum to “Global bifurcation in a virus, defective genomes, satellite RNAs tripartite system: Breakdown of a coexistence quasi-neutral curve” [Chaos Solitons and Fractals 192 (2025) 116037]","authors":"Oriol Llopis-Almela,J. Tomás Lázaro,Santiago F. Elena,Josep Sardanyés","doi":"10.1016/j.chaos.2026.119324","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.119324","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"466 1","pages":"119324"},"PeriodicalIF":7.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149150565","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":"Polarization-controlled switching of pulse regimes in spatiotemporal mode-locked fiber laser via a hybrid saturable absorber","authors":"Honglin Wen ,&nbsp;Bo Gao ,&nbsp;Luyao Zhou ,&nbsp;Qi Li ,&nbsp;Yingying Li ,&nbsp;Feihong Qiao ,&nbsp;Bolin Qu ,&nbsp;Ge Wu ,&nbsp;Lie Liu","doi":"10.1016/j.chaos.2026.118099","DOIUrl":"10.1016/j.chaos.2026.118099","url":null,"abstract":"<div><div>We present an operation switchable spatiotemporal mode-locked fiber laser using a hybrid saturable absorber. The laser cavity incorporates a single-mode fiber-graded-index multimode fiber-single-mode fiber structure acting as an artificial saturable absorber, combined with the nonlinear polarization rotation mechanism. The proposed hybrid saturable absorber enables switching among multimode Q-switching, Q-switched mode-locking, and spatiotemporal mode-locking solely by adjusting the polarization controller at a fixed pump power. We demonstrate that under 800 mW pumping, the laser evolves via polarization tuning from a 48.24 kHz Q-switching state to a Q-switched mode-locking regime featuring mode-locked pulses at 18.72 MHz nested within a Q-switched envelope of 46.88 kHz, and finally to stable spatiotemporal mode-locking at 18.72 MHz. This operational flexibility is attributed to the tunable intracavity loss modulation induced by the hybrid saturable absorber mechanism. Moreover, numerical simulations of the intracavity pulse evolution further confirm the critical role of the hybrid saturable absorber. To the best of our knowledge, this study for the first time achieves various operation regimes solely through polarization control at constant pump power using the hybrid saturable absorber, thus offering a uniquely flexible platform for diverse pulse outputs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118099"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777178","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 geometry-based secure robust switched control strategy for a straight-curved mixed road lattice hydrodynamic model with jerk dynamics and cyber-attacks","authors":"Cong Zhai ,&nbsp;Weitiao Wu ,&nbsp;Yingping Xiao ,&nbsp;Jiyong Zhang ,&nbsp;Min Zhai ,&nbsp;Yingzi Wu","doi":"10.1016/j.chaos.2026.118056","DOIUrl":"10.1016/j.chaos.2026.118056","url":null,"abstract":"<div><div>Intelligent connected vehicles (ICVs) can achieve efficient information exchange and collaboration with nearby vehicles with the implementation of deep integration of contemporary interactions and network infrastructures, thereby enhancing energy efficiency, comfort, and traffic efficiency during the driving process. However, the open communication environment is prone to serious cybersecurity threats, where attackers could exploit vulnerabilities to maliciously manipulate traffic information in the vehicle perception layer, severely jeopardising road safety. Additionally, urban road networks exhibit complex and variable geometric features, often comprising hybrid road forms such as straight and curved segments, and such discontinuous geometric features often induce jerky acceleration and deceleration. To tackle these challenges, we propose a straight-curved mixed road lattice hydrodynamic model simultaneously considering both jerk dynamics and malevolent cyber-attacks. First, according to the H-infinity norm as the basis for the transition function requirement and the Routh-Hurwitz criteria, the sufficient conditions for the stability of the new model are determined; moreover, when the requirements for stability are not fulfilled, while integrating the proportion of different geometric roads in hybrid scenarios, a geometry-based secure robust switcher is produced that takes into account the distinction between the estimation optimal and current flux. Results confirmed by Bode diagram examination that the proposed control approach works to minimize traffic oscillation induced by malevolent cyber-attacks and traffic jerk. Finally, we conducted a series of computational experiments by employing periodic boundary constraints. Results reveal that the cyber-attack intensity factor, the traffic jerk coefficient and the control gain term exert fundamentally distinct impacts on the stability of traffic flow: the latter are positive, while the remaining are negative. These findings align with the theoretical inquiry stated above.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118056"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777183","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":"Fractal Games","authors":"Daeho Lee","doi":"10.1016/j.chaos.2026.118151","DOIUrl":"10.1016/j.chaos.2026.118151","url":null,"abstract":"<div><div>This study introduces Fractal Games, a game-theoretic framework designed to formalize hierarchical recursion within noncooperative antagonistic systems. Traditional equilibrium models capture only local stability, overlooking how stress accumulates and amplifies across layers. The framework establishes sufficient conditions under which lower-level boundary equilibria persist upward as internal stress, leading to endogenous acceleration and a cascading collapse without the need for external shocks. By linking static persistence to dynamic amplification, the model demonstrates how hierarchy alone can reshape the set of feasible equilibria and induce fundamental structural bifurcations. Numerical simulations successfully reproduce these effects and identify four key control levers that mitigate upward propagation: cross-cost relief, stress-saturation caps, weight diversification, and defender incentives. Collectively, these findings offer a unified and rigorous account of how hierarchical organization can transform local balance into system-wide failure, and how targeted interventions can effectively stabilize hierarchical systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118151"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279148","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":"Dynamical characteristics of internal gravity waves in fluid layers with the emergence of mixed solitons","authors":"Muhammad Aamir Ali ,&nbsp;Umair Asghar ,&nbsp;Waqas Ali Faridi ,&nbsp;Mohammad Asadullah ,&nbsp;Abdul-Majid Wazwaz","doi":"10.1016/j.chaos.2026.118142","DOIUrl":"10.1016/j.chaos.2026.118142","url":null,"abstract":"<div><div>The Kakutani–Matsuuchi (KM) equation is a reduced nonlinear model for the propagation of internal gravity waves in stratified fluids with variable density. These waves exhibit rich nonlinear dynamics and can form a variety of solitary wave structures. In this work, the improved modified Sardar sub-equation method (IMSSEM) is applied to derive exact analytical traveling wave solutions of the <span><math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional KM equation. By reducing the governing nonlinear partial differential equation to an associated ordinary differential equation, the IMSSEM provides a systematic and efficient framework for constructing exact solutions. A wide range of localized wave profiles is obtained, including bright, dark, smooth periodic, periodic bright, anti-bell-shaped, mixed bright–dark, and double-notch dark soliton solutions. These solutions are illustrated through two- and three-dimensional, contour, and density plots, offering clear insight into their structural and propagation characteristics and demonstrating the flexibility of the IMSSEM. In addition, a comprehensive dynamical analysis is conducted using phase portraits, Hamiltonian energy-level curves, bifurcation diagrams, sensitivity analysis, and forced dynamical studies. The results reveal complex behaviors, including transitions from regular motion to chaotic-like dynamics and the emergence of multistability, indicating strong sensitivity to initial conditions. These findings enhance the analytical understanding of nonlinear internal wave dynamics and provide useful insight into nonlinear and chaotic behavior in complex physical and engineering systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118142"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279149","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":"Cross-domain traffic hysteresis and stability transitions in mixed traffic flow under cognitive uncertainty dynamics","authors":"Shuaiyang Jiao ,&nbsp;Aizeng Li ,&nbsp;Weizhe Meng ,&nbsp;Qizheng Pei ,&nbsp;Pei Jin","doi":"10.1016/j.chaos.2026.118070","DOIUrl":"10.1016/j.chaos.2026.118070","url":null,"abstract":"<div><div>To overcome the limitations of the decoupled lateral-longitudinal dynamics assumption in traditional models, this study proposes an entropy-coupled car-following model that combines Bayesian intent inference with cognitive uncertainty. By employing a mean-field approximation, we model lateral disturbances from human-driven vehicles in adjacent lanes as a stochastic environmental field. The core contribution lies in introducing an entropy relaxation mechanism to characterize the perception of lateral intent uncertainty by connected autonomous vehicles (CAVs) and constructing a nonlinear feedback mechanism based on a smooth acceleration saturation function. Stability analysis and numerical simulations show that high-intensity intent uncertainty induces traffic hysteresis and leads to a decline in capacity. Phase transition analysis reveals that the hesitant start mechanism modeled by the smooth saturation function causes the actual critical point of macroscopic traffic breakdown to deviate from the linear theoretical prediction, exhibiting a stabilization effect. Finally, a comprehensive sensitivity analysis of control gain attenuation, acceleration constraints, and entropy relaxation time reveals their nonlinear regulatory mechanisms on system stability. In particular, the study confirms that introducing moderate historical information buffering into the CAV control system can effectively suppress traffic congestion. These findings provide a new perspective for designing robust CAV control systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118070"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386421","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":"Geometry of almost-conserved quantities in symplectic maps","authors":"Tim Zolkin ,&nbsp;Sergei Nagaitsev ,&nbsp;Ivan Morozov ,&nbsp;Sergei Kladov","doi":"10.1016/j.chaos.2026.118059","DOIUrl":"10.1016/j.chaos.2026.118059","url":null,"abstract":"<div><div>Noether’s theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the emergence of exact invariants from continuous symmetries, and the appearance of approximate invariants from discrete symmetries associated with reversibility in symplectic maps. We demonstrate that by constructing approximating functions that preserve these discrete symmetries order by order, one can systematically uncover hidden structures, closely echoing Noether’s framework. The resulting unified function, constructed from the map coefficients, produces phase portraits, rotation numbers, and tune footprints that closely agree with numerical tracking over wide parameter ranges, thereby offering a compact representation of near-integrable dynamics.</div><div>Using the symmetric form of the map as a flexible test case, we benchmark the perturbative construction against established techniques, including the Lie algebra method for twist coefficients. To resolve the inherent ambiguity in the perturbation series, we introduce an averaging procedure that naturally leads to a resonant theory — capable of treating rational rotation numbers and small-denominator divergences. This enables an accurate and structured description of low-order resonances, including singular and non-singular features in the quadratic and cubic Hénon maps. We also explore the recovery of exact invariants in integrable cases of McMillan and Suris mappings, showing that the method reproduces the correct behavior when such structure is present. Comparisons with the Square Matrix method reveal that while both approaches satisfy local constraints, our technique provides greater accuracy and robustness in resonant and strongly nonlinear regimes. The approach is systematic, requiring only linear algebra and integrals of elementary functions, yet it yields results in striking agreement with both theory and numerical experiment.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118059"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386422","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":"Compact Landau–Khalatnikov FeFET polarization model and its 5D hyperchaotic integration with multi-scroll attractors","authors":"Mehmet Sağbaş ,&nbsp;Shahram Minaei","doi":"10.1016/j.chaos.2026.118051","DOIUrl":"10.1016/j.chaos.2026.118051","url":null,"abstract":"<div><div>The demand for high-dimensional and complex chaotic systems for secure communication and cryptography applications has motivated the development of novel hardware-based oscillators. This paper presents a novel five-dimensional (5D) chaotic system developed by integrating a compact, physics-based Ferroelectric Field-Effect Transistor (FeFET) polarization model within a Lorenz-type core. The proposed FeFET model, which is based on the Landau–Khalatnikov (LK) equation, is first presented and comprehensively tested. It captures the important hysteretic polarization dynamics that give it both nonlinearity and memory. A comprehensive analysis, including phase portraits, equilibrium point stability, and Lyapunov exponents, shows that the resulting 5D system is chaotic. In addition, a Parallel Fractal Algorithm (PFA) is used to systematically generate multi-scroll attractors through one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) folding. The results demonstrate that this PFA-driven topological folding not only scales the attractor complexity up to 256 distinct scrolls but also induces a dynamic transition from simple chaos to hyperchaos driven by high topological complexity. To validate practical feasibility, the proposed system is experimentally implemented using an STM32 microcontroller. Furthermore, its cryptographic robustness is demonstrated through a 3D biomedical volume encryption application. These results confirm that the proposed system is a promising option for use in image encryption and secure communication systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118051"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386423","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 discretization theorems for forced linear and nonlinear coupled oscillators","authors":"Stefano Disca,&nbsp;Vincenzo Coscia","doi":"10.1016/j.chaos.2026.118086","DOIUrl":"10.1016/j.chaos.2026.118086","url":null,"abstract":"<div><div>We prove the holding of chaos in the sense of Li–Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force, also giving an example of a discrete map that is Li–Yorke chaotic but not topologically transitive. Analytical results are generalized to a modular definition of the problem and to a system of nonlinear oscillators described by polynomial potentials in one coordinate. We perform numerical simulations looking for a strange attractor of the system; furthermore, we perform a bifurcation analysis of the system presenting 1D and 2D bifurcation diagrams, together with spectra of Lyapunov exponents and basins of attraction.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118086"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386379","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}