Pub Date : 2026-05-01Epub Date: 2026-01-27DOI: 10.1016/j.chaos.2026.117946
Hui-Cong Zhang, Ming-Xu Yang, Zhi-Xuan Wang
This paper numerically investigates the existence, stability, and propagation dynamics of vector vortex solitons (VVS), comprising two incoherently coupled vortices with different topological charges (e.g., |l1| ≤ 1 and |l2| ≥ 3) in nematic liquid crystals with cylindrical symmetry. An analysis of scaling transformation demonstrates that VVS with identical power and beamwidth ratios are physically equivalent under varying propagation constants and nonlocality parameters. Linear stability analysis reveals that the azimuthal instability of the high-order vortex can be suppressed and even eliminated due to the presence of the other low-order vortex, including the fundamental soliton. VVS with opposite-sign topological charges, particularly the (−1,l2) states, can achieve full stability within specific power ratio intervals near the equal beamwidth point. Numerical simulations for perturbed VVS confirm the predictions of linear stability analysis.
{"title":"Existence and stability of vector vortex solitons in nematic liquid crystals","authors":"Hui-Cong Zhang, Ming-Xu Yang, Zhi-Xuan Wang","doi":"10.1016/j.chaos.2026.117946","DOIUrl":"10.1016/j.chaos.2026.117946","url":null,"abstract":"<div><div>This paper numerically investigates the existence, stability, and propagation dynamics of vector vortex solitons (VVS), comprising two incoherently coupled vortices with different topological charges (e.g., |<em>l</em><sub>1</sub>| ≤ 1 and |<em>l</em><sub>2</sub>| ≥ 3) in nematic liquid crystals with cylindrical symmetry. An analysis of scaling transformation demonstrates that VVS with identical power and beamwidth ratios are physically equivalent under varying propagation constants and nonlocality parameters. Linear stability analysis reveals that the azimuthal instability of the high-order vortex can be suppressed and even eliminated due to the presence of the other low-order vortex, including the fundamental soliton. VVS with opposite-sign topological charges, particularly the (−1,<em>l</em><sub>2</sub>) states, can achieve full stability within specific power ratio intervals near the equal beamwidth point. Numerical simulations for perturbed VVS confirm the predictions of linear stability analysis.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117946"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072022","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}
Pub Date : 2026-05-01Epub Date: 2026-01-14DOI: 10.1016/j.chaos.2026.117914
Zbigniew Czechowski , Luciano Telesca
Asymmetry in persistence introduces an additional directed force that alters the dynamics of stochastic processes, potentially affecting the behavior of extremes in their realizations (time series). In this work, we investigate these effect, unexplored so far, using a modified Langevin model that incorporates an asymmetric persistence mechanism. Extremes are defined through run theory and analyzed using informational measures, alongside examining the topological properties of visibility graphs constructed from the point processes of extremes. Our results reveal a systematic influence of asymmetry on the behavior of extremes—both their size and magnitude decrease with increasing asymmetry, while their degree of order, quantified by Shannon entropy, increases.
{"title":"Effect of asymmetric persistence in the modified nonlinear Langevin model on behavior of extremes in generated time series","authors":"Zbigniew Czechowski , Luciano Telesca","doi":"10.1016/j.chaos.2026.117914","DOIUrl":"10.1016/j.chaos.2026.117914","url":null,"abstract":"<div><div>Asymmetry in persistence introduces an additional directed force that alters the dynamics of stochastic processes, potentially affecting the behavior of extremes in their realizations (time series). In this work, we investigate these effect, unexplored so far, using a modified Langevin model that incorporates an asymmetric persistence mechanism. Extremes are defined through run theory and analyzed using informational measures, alongside examining the topological properties of visibility graphs constructed from the point processes of extremes. Our results reveal a systematic influence of asymmetry on the behavior of extremes—both their size and magnitude decrease with increasing asymmetry, while their degree of order, quantified by Shannon entropy, increases.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117914"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976352","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}
Pub Date : 2026-05-01Epub Date: 2026-01-23DOI: 10.1016/j.chaos.2026.117983
Wenping Wang, Huanying Xu
In this paper, a fractional discrete Chua’s system exhibiting both chaotic and hyperchaotic behaviors is proposed. Stability analysis is conducted for both commensurate and incommensurate fractional orders at equilibrium points, supported by numerical calculations and simulations. The critical point of Hopf bifurcation is determined for commensurate orders. To understand how order asymmetry influences the dynamic complexity of a fractional system, a principle named Synchronous Order Maximum Entropy Theorem is proposed. The study focuses on diverse attractors, including quasi-periodic, chaotic, periodic, and hyperchaotic types, as well as the coexistence of multiple attractors under specific parameter settings. Notably, the system demonstrates the coexistence of offset-boosted and initial-switched boosting behaviors, which are rarely observed in discrete systems. Furthermore, synchronization of the fractional discrete Chua’s system is achieved. The results demonstrate that the proposed fractional discrete Chua’s system exhibits remarkably rich and complex dynamical characteristics. Finally, an image encryption application based on this system is presented to illustrate its practical potential.
{"title":"Dynamical analysis of a fractional discrete-time Chua’s circuit system","authors":"Wenping Wang, Huanying Xu","doi":"10.1016/j.chaos.2026.117983","DOIUrl":"10.1016/j.chaos.2026.117983","url":null,"abstract":"<div><div>In this paper, a fractional discrete Chua’s system exhibiting both chaotic and hyperchaotic behaviors is proposed. Stability analysis is conducted for both commensurate and incommensurate fractional orders at equilibrium points, supported by numerical calculations and simulations. The critical point of Hopf bifurcation is determined for commensurate orders. To understand how order asymmetry influences the dynamic complexity of a fractional system, a principle named Synchronous Order Maximum Entropy Theorem is proposed. The study focuses on diverse attractors, including quasi-periodic, chaotic, periodic, and hyperchaotic types, as well as the coexistence of multiple attractors under specific parameter settings. Notably, the system demonstrates the coexistence of offset-boosted and initial-switched boosting behaviors, which are rarely observed in discrete systems. Furthermore, synchronization of the fractional discrete Chua’s system is achieved. The results demonstrate that the proposed fractional discrete Chua’s system exhibits remarkably rich and complex dynamical characteristics. Finally, an image encryption application based on this system is presented to illustrate its practical potential.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117983"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033514","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}
Pub Date : 2026-05-01Epub Date: 2026-01-23DOI: 10.1016/j.chaos.2026.117967
H.A. Erbay, S. Erbay
In this study we consider traveling wave solutions of a nonlinear dispersive wave equation involving the fourth-order time derivative term. We first discuss existence of traveling wave solutions to the dispersive wave equation with a quadratic nonlinearity and report sech-type solitary wave solutions. Using asymptotic expansion techniques we derive the well-known unidirectional nonlinear dispersive wave equations for small amplitude waves. The KdV equation models the propagation of long acoustic waves, while the NLS equation models the evolution of the envelope of short optic waves. We also show that when a long-wave–short-wave resonance condition is satisfied, a coupled system of equations describes the nonlinear interaction between long acoustic waves and short optic waves. We study traveling wave solutions of the asymptotic models derived to assess the relative importance of nonlocality in time with respect to nonlocality in space.
{"title":"Traveling wave solutions of the doubly regularized nonlinear Boussinesq equation","authors":"H.A. Erbay, S. Erbay","doi":"10.1016/j.chaos.2026.117967","DOIUrl":"10.1016/j.chaos.2026.117967","url":null,"abstract":"<div><div>In this study we consider traveling wave solutions of a nonlinear dispersive wave equation involving the fourth-order time derivative term. We first discuss existence of traveling wave solutions to the dispersive wave equation with a quadratic nonlinearity and report sech-type solitary wave solutions. Using asymptotic expansion techniques we derive the well-known unidirectional nonlinear dispersive wave equations for small amplitude waves. The KdV equation models the propagation of long acoustic waves, while the NLS equation models the evolution of the envelope of short optic waves. We also show that when a long-wave–short-wave resonance condition is satisfied, a coupled system of equations describes the nonlinear interaction between long acoustic waves and short optic waves. We study traveling wave solutions of the asymptotic models derived to assess the relative importance of nonlocality in time with respect to nonlocality in space.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117967"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033515","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}
Pub Date : 2026-05-01Epub Date: 2026-01-22DOI: 10.1016/j.chaos.2026.117944
N.P. Sasikumar, P. Balasubramaniam
Modeling chaotic synchronization from data is challenging because standard approaches such as NeuralODEs and PINNs lose stability, degrade under noise, and provide little insight into the underlying dynamics. This article introduce a Koopman Physics-Informed Neural Network (Koopman-PINN) that combines Koopman operator embeddings with physics-based residual training to learn accurate and interpretable representations of coupled chaotic oscillators. The model yields clean spectral modes, robust phase-space reconstructions, and reliable separation of synchronized and desynchronized behavior. Experiments on coupled Rössler oscillators show that Koopman-PINN maintains stability over long prediction horizons, generalizes to unseen trajectories, and outperforms NeuralODEs and classical PINNs while providing quantitative spectral features unavailable in existing methods. This framework offers a data-efficient and interpretable approach for analyzing nonlinear synchronization dynamics.
{"title":"Modeling chaotic synchronization dynamics using Koopman Physics-Informed Neural Networks","authors":"N.P. Sasikumar, P. Balasubramaniam","doi":"10.1016/j.chaos.2026.117944","DOIUrl":"10.1016/j.chaos.2026.117944","url":null,"abstract":"<div><div>Modeling chaotic synchronization from data is challenging because standard approaches such as NeuralODEs and PINNs lose stability, degrade under noise, and provide little insight into the underlying dynamics. This article introduce a Koopman Physics-Informed Neural Network (Koopman-PINN) that combines Koopman operator embeddings with physics-based residual training to learn accurate and interpretable representations of coupled chaotic oscillators. The model yields clean spectral modes, robust phase-space reconstructions, and reliable separation of synchronized and desynchronized behavior. Experiments on coupled Rössler oscillators show that Koopman-PINN maintains stability over long prediction horizons, generalizes to unseen trajectories, and outperforms NeuralODEs and classical PINNs while providing quantitative spectral features unavailable in existing methods. This framework offers a data-efficient and interpretable approach for analyzing nonlinear synchronization dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117944"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033527","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}
Pub Date : 2026-05-01Epub Date: 2026-01-24DOI: 10.1016/j.chaos.2026.117939
Nan Wang , Xiaoying Tang , Shunyu Liu , Lu Tian , Yu-Xuan Ren , Yi Liang
Non-diffracting beams are a special type of optical field that can resist diffraction and maintain a constant transverse profile during propagation. Self-similar beams, on the other hand, are a special type of optical field that maintains the shape of the transverse intensity profile but scales in size during propagation. Although they are not the same, perfect self-similar Bessel beams (PSBBs) as an intermediate mode between non-diffracting beams and self-similar beams, maintain a strictly self-similar transverse profile and constant intensity during propagation. Here, we start from the linear propagation dynamics of PSBBs, and the nonlinear self-focusing in a biased photorefractive strontium-barium niobate (SBN) crystal, and demonstrate the optical manipulation of Rayleigh particles with PSBBs. The power flow, trapping force, and torque of PSBBs all decrease with the propagation distance, while the orbital angular momentum (OAM) and corresponding angular momentum density (AMD) remain constant during propagation. In a nonlinear medium, the intensity of the beam shows an alternating multi-foci along the propagation direction, characterized by periodic local enhancement and broadening. The attenuation rate of the trapping force is fast and the propagation stability is much lower than that in the linear case. Our work not only reveals the unique properties of PSBBs but also has significant implications for in-depth understanding of the optical field control in nonlinear media and the construction of advanced photonic devices.
{"title":"Propagation dynamics and optical manipulation of perfect self-similar Bessel beams in linear and nonlinear regimes","authors":"Nan Wang , Xiaoying Tang , Shunyu Liu , Lu Tian , Yu-Xuan Ren , Yi Liang","doi":"10.1016/j.chaos.2026.117939","DOIUrl":"10.1016/j.chaos.2026.117939","url":null,"abstract":"<div><div>Non-diffracting beams are a special type of optical field that can resist diffraction and maintain a constant transverse profile during propagation. Self-similar beams, on the other hand, are a special type of optical field that maintains the shape of the transverse intensity profile but scales in size during propagation. Although they are not the same, perfect self-similar Bessel beams (PSBBs) as an intermediate mode between non-diffracting beams and self-similar beams, maintain a strictly self-similar transverse profile and constant intensity during propagation. Here, we start from the linear propagation dynamics of PSBBs, and the nonlinear self-focusing in a biased photorefractive strontium-barium niobate (SBN) crystal, and demonstrate the optical manipulation of Rayleigh particles with PSBBs. The power flow, trapping force, and torque of PSBBs all decrease with the propagation distance, while the orbital angular momentum (OAM) and corresponding angular momentum density (AMD) remain constant during propagation. In a nonlinear medium, the intensity of the beam shows an alternating multi-foci along the propagation direction, characterized by periodic local enhancement and broadening. The attenuation rate of the trapping force is fast and the propagation stability is much lower than that in the linear case. Our work not only reveals the unique properties of PSBBs but also has significant implications for in-depth understanding of the optical field control in nonlinear media and the construction of advanced photonic devices.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117939"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048056","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}
Pub Date : 2026-05-01Epub Date: 2026-01-17DOI: 10.1016/j.chaos.2026.117930
Wasim Sajjad, Yi Jiang
The identification of influential nodes in complex networks is a fundamental problem in network science with significant implications for infrastructure resilience, epidemic control, biological discovery and marketing strategies. Traditional centrality measures provide valuable insights but are limited by their reliance on global structures or shortest-path distances. Gravity-based models have been proposed to overcome these gaps by integrating node properties with distance-based interactions, yet most existing formulations are global in scope and computationally demanding. In this study, we propose a novel local resistance distance based gravity model (LRGM) for the identification of influential nodes in complex networks. Unlike global approaches, LRGM restricts interactions to nodes within a truncated resistance distance radius, thereby capturing localized influence while reducing computational complexity. Experimental evaluations demonstrate that the efficiency of LRGM is better than the global centrality measures.
{"title":"Comparative analysis of local variant resistance distance-based gravity model for the identification of influential nodes","authors":"Wasim Sajjad, Yi Jiang","doi":"10.1016/j.chaos.2026.117930","DOIUrl":"10.1016/j.chaos.2026.117930","url":null,"abstract":"<div><div>The identification of influential nodes in complex networks is a fundamental problem in network science with significant implications for infrastructure resilience, epidemic control, biological discovery and marketing strategies. Traditional centrality measures provide valuable insights but are limited by their reliance on global structures or shortest-path distances. Gravity-based models have been proposed to overcome these gaps by integrating node properties with distance-based interactions, yet most existing formulations are global in scope and computationally demanding. In this study, we propose a novel local resistance distance based gravity model (LRGM) for the identification of influential nodes in complex networks. Unlike global approaches, LRGM restricts interactions to nodes within a truncated resistance distance radius, thereby capturing localized influence while reducing computational complexity. Experimental evaluations demonstrate that the efficiency of LRGM is better than the global centrality measures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117930"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995114","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}
Pub Date : 2026-05-01Epub Date: 2026-01-13DOI: 10.1016/j.chaos.2026.117874
Ivan D. Kolesnikov, Nadezhda Semenova
Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming a neural network into a tangible device. In terms of hardware neural networks, it is more important to consider not only the effect of noise on the input signal, but also the effect of internal noise coming from various network components. In this paper, we investigate how internal noise affects the final performance of feedforward neural networks (FNN) and echo state networks (ESN) during the training of neural networks. The types of noise considered in this paper were originally inspired by a real optical implementation of a neural network. However, these types were subsequently generalized to enhance the applicability of our findings on a broader scale. The noise types considered include additive and multiplicative noise, which depend on how noise influences each individual neuron, and common and uncommon noise, which pertains to the impact of noise on groups of neurons (such as the hidden layer of FNNs or the reservoir of ESNs). In this paper, we demonstrate that, in most cases, both deep and echo state networks benefit from internal noise during training, as it enhances their resilience to noise. Consequently, the testing performance at the same noise intensities is significantly higher for networks trained with noise than for those trained without it. Only multiplicative common noise during training has almost no impact on both deep and recurrent networks.
{"title":"Internal noise in analog neural networks helps with learning","authors":"Ivan D. Kolesnikov, Nadezhda Semenova","doi":"10.1016/j.chaos.2026.117874","DOIUrl":"10.1016/j.chaos.2026.117874","url":null,"abstract":"<div><div>Recently, the field of hardware neural networks has been actively developing, where neurons and their connections are not simulated on a computer but are implemented at the physical level, transforming a neural network into a tangible device. In terms of hardware neural networks, it is more important to consider not only the effect of noise on the input signal, but also the effect of internal noise coming from various network components. In this paper, we investigate how internal noise affects the final performance of feedforward neural networks (FNN) and echo state networks (ESN) during the training of neural networks. The types of noise considered in this paper were originally inspired by a real optical implementation of a neural network. However, these types were subsequently generalized to enhance the applicability of our findings on a broader scale. The noise types considered include additive and multiplicative noise, which depend on how noise influences each individual neuron, and common and uncommon noise, which pertains to the impact of noise on groups of neurons (such as the hidden layer of FNNs or the reservoir of ESNs). In this paper, we demonstrate that, in most cases, both deep and echo state networks benefit from internal noise during training, as it enhances their resilience to noise. Consequently, the testing performance at the same noise intensities is significantly higher for networks trained with noise than for those trained without it. Only multiplicative common noise during training has almost no impact on both deep and recurrent networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117874"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950160","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}
Pub Date : 2026-05-01Epub Date: 2026-01-12DOI: 10.1016/j.chaos.2025.117853
Jiani Ren , Jiaquan Xie , Wei Shi , Zhonghua Wang , Jianguo Liang
This paper explores the multi-steady-state vibration mechanism of a fractional-order quarter-car suspension under multi-frequency excitation. First, the multiscale method is used to derive an approximate analytical solution for multi-steady-state vibration, and stability criteria for steady-state responses are established by combining the Hartman-Grobman theorem and Routh-Hurwitz criterion. The method's accuracy is verified by comparing the analytical solution with the attraction domain from cell mapping numerical simulation. Analysis shows the system has notable multi-steady-state features in a specific frequency coupling interval; its stable and unstable solutions undergo bifurcation evolution with frequency ratio changes. Stiffness-hardening suspensions can exhibit bistable, tristable, or quadri-stable periodic vibrations, while stiffness-softening ones, though having four steady-state periodic vibration modes, show dynamic responses with unbounded regions and fractal characteristics. Finally, the regulation mechanism of fractional-order parameters on saddle-node (SN) bifurcation characteristics is investigated, and the intrinsic relationship between parameter variations and the evolution of the number of solution branches is clarified. Results indicate reasonable adjustments of fractional-order damping parameters can effectively control the stable support range and attraction domain distribution, providing theoretical support for revealing the multi-steady-state vibration mechanism of fractional-order suspensions and engineering references for optimizing suspension dynamic performance.
{"title":"Analysis of the multistable vibration mechanism of a fractional-order quarter-car suspension under multi-frequency excitation","authors":"Jiani Ren , Jiaquan Xie , Wei Shi , Zhonghua Wang , Jianguo Liang","doi":"10.1016/j.chaos.2025.117853","DOIUrl":"10.1016/j.chaos.2025.117853","url":null,"abstract":"<div><div>This paper explores the multi-steady-state vibration mechanism of a fractional-order quarter-car suspension under multi-frequency excitation. First, the multiscale method is used to derive an approximate analytical solution for multi-steady-state vibration, and stability criteria for steady-state responses are established by combining the Hartman-Grobman theorem and Routh-Hurwitz criterion. The method's accuracy is verified by comparing the analytical solution with the attraction domain from cell mapping numerical simulation. Analysis shows the system has notable multi-steady-state features in a specific frequency coupling interval; its stable and unstable solutions undergo bifurcation evolution with frequency ratio changes. Stiffness-hardening suspensions can exhibit bistable, tristable, or quadri-stable periodic vibrations, while stiffness-softening ones, though having four steady-state periodic vibration modes, show dynamic responses with unbounded regions and fractal characteristics. Finally, the regulation mechanism of fractional-order parameters on saddle-node (SN) bifurcation characteristics is investigated, and the intrinsic relationship between parameter variations and the evolution of the number of solution branches is clarified. Results indicate reasonable adjustments of fractional-order damping parameters can effectively control the stable support range and attraction domain distribution, providing theoretical support for revealing the multi-steady-state vibration mechanism of fractional-order suspensions and engineering references for optimizing suspension dynamic performance.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117853"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950161","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}
Pub Date : 2026-05-01Epub Date: 2026-01-21DOI: 10.1016/j.chaos.2026.117954
R. Cárdenas-Sabando , M.G. Cosenza , J.C. González-Avella
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and reconnection based on node similarity, we systematically explore how homophilic and heterophilic interactions influence network topology. A mean-field approximation for the stationary density of active links — those connecting nodes in different states — is developed to determine the conditions under which fragmentation occurs. Analytical results closely agree with numerical simulations. To distinguish community formation from fragmentation, we introduce order parameters that integrate modularity and connectivity. This enables the characterization of three distinct network phases on the rewiring parameter space: (i) random connectivity, (ii) community structure, and (iii) fragmentation. Community structure emerges only under moderate homophily, while extreme homophily or heterophily lead to fragmentation or random networks, respectively. These findings demonstrate that adaptive rewiring alone, independent of node dynamics, can drive complex structural self-organization, with implications for social, technological, and ecological systems where node attributes are intrinsically stable.
{"title":"Structural transitions induced by adaptive rewiring in networks with fixed states","authors":"R. Cárdenas-Sabando , M.G. Cosenza , J.C. González-Avella","doi":"10.1016/j.chaos.2026.117954","DOIUrl":"10.1016/j.chaos.2026.117954","url":null,"abstract":"<div><div>We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and reconnection based on node similarity, we systematically explore how homophilic and heterophilic interactions influence network topology. A mean-field approximation for the stationary density of active links — those connecting nodes in different states — is developed to determine the conditions under which fragmentation occurs. Analytical results closely agree with numerical simulations. To distinguish community formation from fragmentation, we introduce order parameters that integrate modularity and connectivity. This enables the characterization of three distinct network phases on the rewiring parameter space: (i) random connectivity, (ii) community structure, and (iii) fragmentation. Community structure emerges only under moderate homophily, while extreme homophily or heterophily lead to fragmentation or random networks, respectively. These findings demonstrate that adaptive rewiring alone, independent of node dynamics, can drive complex structural self-organization, with implications for social, technological, and ecological systems where node attributes are intrinsically stable.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117954"},"PeriodicalIF":5.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014460","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}
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