This paper proposes a spatial public goods game model incorporating a dual-pool coupling mechanism to explore how delayed gratification and resource accumulation influence cooperation. Unlike traditional instant allocation models, we introduce an independent reward pool where resources undergo nonlinear amplification over time and are distributed based on historical contribution records. Simulation results indicate that this mechanism significantly promotes cooperation, particularly in harsh environments where traditional cooperation approaches fail. We identify two distinct ecological roles for investors: acting as survivors that form defensive clusters in low-synergy conditions, and serving as symbiotic cores that support diverse communities in high-synergy conditions. The memory-based exclusivity barrier effectively resolves the waning-moon effect by preventing defectors from appropriating accumulated wealth. Furthermore, parametric analysis indicates that the system exhibits asymmetric robustness, being highly sensitive to resource multiplication efficiency and distribution ratios but tolerant to investment costs. These findings provide theoretical insights into the design of sustainable social incentive systems.
{"title":"The impact of a dynamic reward pool mechanism based on historical memory on the cooperative evolution of spatial public goods games","authors":"Yong Shen, Lingye Zeng, Hongwei Kang, Xingping Sun, Qingyi Chen, Chengzhi Feng","doi":"10.1016/j.chaos.2026.117990","DOIUrl":"10.1016/j.chaos.2026.117990","url":null,"abstract":"<div><div>This paper proposes a spatial public goods game model incorporating a dual-pool coupling mechanism to explore how delayed gratification and resource accumulation influence cooperation. Unlike traditional instant allocation models, we introduce an independent reward pool where resources undergo nonlinear amplification over time and are distributed based on historical contribution records. Simulation results indicate that this mechanism significantly promotes cooperation, particularly in harsh environments where traditional cooperation approaches fail. We identify two distinct ecological roles for investors: acting as survivors that form defensive clusters in low-synergy conditions, and serving as symbiotic cores that support diverse communities in high-synergy conditions. The memory-based exclusivity barrier effectively resolves the waning-moon effect by preventing defectors from appropriating accumulated wealth. Furthermore, parametric analysis indicates that the system exhibits asymmetric robustness, being highly sensitive to resource multiplication efficiency and distribution ratios but tolerant to investment costs. These findings provide theoretical insights into the design of sustainable social incentive systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117990"},"PeriodicalIF":5.6,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072012","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 : 2026-01-28DOI: 10.1016/j.chaos.2026.117931
Bo Gao , Meng An , Danyang Jia , Xiangfeng Dai , Xingyu Qin , Xingsheng Chen
In light of the dynamic and heterogeneous nature of individual preferences in real-world social interactions, we propose a research framework that integrates reinforcement learning with adaptive weights. In real social systems, interactions among individuals are not heterogeneous, and they exhibit significant preference diversity and context dependence. By introducing dynamic weight evolution, this study characterizes the adaptive processes of individuals in social dilemmas, where weight allocation captures the dual influence of social interaction preferences and feedback from stimuli. The results reveal that this adaptive weighting mechanism effectively sustains high levels of cooperation within the population. In particular, adaptive weights stimulate cooperation through preference selection under high social dilemma strength. Importantly, the evolution of weights leads to a polarization of the strategy within the population, resulting in a stable coexistence of cooperation and defection. Furthermore, the study uncovers the micro-level regulatory role of the weight mechanism in network reciprocity, enriching the theoretical framework of cooperation evolution in complex systems. It provides a new perspective for understanding the formation and evolution of cooperation.
{"title":"Effects of adaptive agent reinforcement learning on cooperation in spatial networks","authors":"Bo Gao , Meng An , Danyang Jia , Xiangfeng Dai , Xingyu Qin , Xingsheng Chen","doi":"10.1016/j.chaos.2026.117931","DOIUrl":"10.1016/j.chaos.2026.117931","url":null,"abstract":"<div><div>In light of the dynamic and heterogeneous nature of individual preferences in real-world social interactions, we propose a research framework that integrates reinforcement learning with adaptive weights. In real social systems, interactions among individuals are not heterogeneous, and they exhibit significant preference diversity and context dependence. By introducing dynamic weight evolution, this study characterizes the adaptive processes of individuals in social dilemmas, where weight allocation captures the dual influence of social interaction preferences and feedback from stimuli. The results reveal that this adaptive weighting mechanism effectively sustains high levels of cooperation within the population. In particular, adaptive weights stimulate cooperation through preference selection under high social dilemma strength. Importantly, the evolution of weights leads to a polarization of the strategy within the population, resulting in a stable coexistence of cooperation and defection. Furthermore, the study uncovers the micro-level regulatory role of the weight mechanism in network reciprocity, enriching the theoretical framework of cooperation evolution in complex systems. It provides a new perspective for understanding the formation and evolution of cooperation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117931"},"PeriodicalIF":5.6,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072017","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 : 2026-01-28DOI: 10.1016/j.chaos.2026.117878
Shahroud Azami
In this paper, we will point out the errors in Formula (1.3). The results of this paper, which depend on Formula (1.3), are restated and proofs are provided.
在本文中，我们将指出公式（1.3）中的误差。对依赖于式（1.3）的本文结果进行了重述并给出了证明。
{"title":"Comment on the paper “Ricci soliton and relativistic thermodynamical fluid spacetime” (Published in Chaos, Solitons and Fractals 194 (2025) 116202)","authors":"Shahroud Azami","doi":"10.1016/j.chaos.2026.117878","DOIUrl":"10.1016/j.chaos.2026.117878","url":null,"abstract":"<div><div>In this paper, we will point out the errors in Formula (1.3). The results of this paper, which depend on Formula (1.3), are restated and proofs are provided.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117878"},"PeriodicalIF":5.6,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072015","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 : 2026-01-28DOI: 10.1016/j.chaos.2026.117986
Chunpeng Du , Zongyang Li , Yali Zhang , Yikang Lu , Attila Szolnoki
Q-learning provides a standard reinforcement learning framework for studying cooperation by specifying how agents update action values from repeated local interactions outcomes. Although previous work has shown that reputation can promote cooperation in such systems, most models introduce reputation by modifying payoffs, encoding it directly in the state or changing partner selection, which makes it difficult to isolate the role of the learning signal itself. Here, we construct the reinforcement signal as a weighted combination of reputation and game payoffs, leaving the game and network structure unchanged. We find that increasing the weight on reputation generally promotes cooperation by consolidating clusters, but this effect is conditional on the learning dynamics. Specifically, this promoting effect vanishes in two regimes: when the learning rate is extremely small, which prevents effective information propagation and when the discount factor approaches one, as distant future expectations obscure the immediate reputational advantage. Outside these limiting cases, the efficacy of reputation in promoting cooperation is attenuated by higher learning rates but amplified by larger discount factors. These results advance the understanding of cooperative dynamics by demonstrating that cooperation can be stabilized through the reputational shaping of learning signals alone, providing critical insights into the interplay between social information and individual learning parameters.
{"title":"Shaping the learning signal in a combined Q-learning rule to improve structured cooperation","authors":"Chunpeng Du , Zongyang Li , Yali Zhang , Yikang Lu , Attila Szolnoki","doi":"10.1016/j.chaos.2026.117986","DOIUrl":"10.1016/j.chaos.2026.117986","url":null,"abstract":"<div><div>Q-learning provides a standard reinforcement learning framework for studying cooperation by specifying how agents update action values from repeated local interactions outcomes. Although previous work has shown that reputation can promote cooperation in such systems, most models introduce reputation by modifying payoffs, encoding it directly in the state or changing partner selection, which makes it difficult to isolate the role of the learning signal itself. Here, we construct the reinforcement signal as a weighted combination of reputation and game payoffs, leaving the game and network structure unchanged. We find that increasing the weight on reputation generally promotes cooperation by consolidating clusters, but this effect is conditional on the learning dynamics. Specifically, this promoting effect vanishes in two regimes: when the learning rate is extremely small, which prevents effective information propagation and when the discount factor approaches one, as distant future expectations obscure the immediate reputational advantage. Outside these limiting cases, the efficacy of reputation in promoting cooperation is attenuated by higher learning rates but amplified by larger discount factors. These results advance the understanding of cooperative dynamics by demonstrating that cooperation can be stabilized through the reputational shaping of learning signals alone, providing critical insights into the interplay between social information and individual learning parameters.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117986"},"PeriodicalIF":5.6,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072013","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 : 2026-01-27DOI: 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":"2026-01-27","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 : 2026-01-27DOI: 10.1016/j.chaos.2026.117913
Sishu Shankar Muni
In this study, we present a predominantly numerical investigation of a novel class of one-dimensional discontinuous dynamical systems, referred to as the generalized ceil map, which combines a power-law nonlinearity with a discontinuous ceiling operation. Despite its simplicity, the map exhibits remarkably rich dynamics, including fixed point stability, robust chaos, and analytically tractable invariant density expressions. Through a detailed investigation of the system’s bifurcation structure, we identify clearly defined stability boundaries (analytically and numerically) and demonstrate the onset of robust chaos in both one and two-parameter spaces involving the nonlinearity exponent , offset parameter , and vertical parameter . Notably, we observe the rare phenomenon of a monotonically increasing Lyapunov exponent within the regime of robust chaos. Analytical expressions for the fixed points and their stability thresholds are derived, allowing us to compute critical parameter values that separate stable and chaotic dynamical regimes. The invariant density function is calculated both numerically and analytically, with the analytical expression becoming asymptotically flat as , aligning well with simulations. We further analyze the role of parameter variations, revealing that increasing the offset disrupts robust chaos and induces periodicity, while changes in have a negligible topological impact and robust chaos persists in such case. We also briefly introduce a similar 1D discontinuous mapping based on the rounding function. These alternative systems show significantly smaller regions of robust chaos and greater susceptibility to periodic windows. Finally, we have explored various types of spatiotemporal patterns observed in the ring-star network configuration including synchronized state, cluster synchronization, and cluster chimera state. To understand the transition of various spatiotemporal patterns with simultaneous variations of the ring and star coupling strengths, we computed a two-parameter regime map in the coupling strength plane highlighting transitions of various novel spatiotemporal patterns.
{"title":"Robust chaos in the generalized ceil map","authors":"Sishu Shankar Muni","doi":"10.1016/j.chaos.2026.117913","DOIUrl":"10.1016/j.chaos.2026.117913","url":null,"abstract":"<div><div>In this study, we present a predominantly numerical investigation of a novel class of one-dimensional discontinuous dynamical systems, referred to as the generalized ceil map, which combines a power-law nonlinearity with a discontinuous ceiling operation. Despite its simplicity, the map exhibits remarkably rich dynamics, including fixed point stability, robust chaos, and analytically tractable invariant density expressions. Through a detailed investigation of the system’s bifurcation structure, we identify clearly defined stability boundaries (analytically and numerically) and demonstrate the onset of robust chaos in both one and two-parameter spaces involving the nonlinearity exponent <span><math><mi>α</mi></math></span>, offset parameter <span><math><mi>c</mi></math></span>, and vertical parameter <span><math><mi>A</mi></math></span>. Notably, we observe the rare phenomenon of a monotonically increasing Lyapunov exponent within the regime of robust chaos. Analytical expressions for the fixed points and their stability thresholds are derived, allowing us to compute critical parameter values that separate stable and chaotic dynamical regimes. The invariant density function <span><math><mrow><mi>ρ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is calculated both numerically and analytically, with the analytical expression becoming asymptotically flat as <span><math><mrow><mi>α</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, aligning well with simulations. We further analyze the role of parameter variations, revealing that increasing the offset <span><math><mi>c</mi></math></span> disrupts robust chaos and induces periodicity, while changes in <span><math><mi>A</mi></math></span> have a negligible topological impact and robust chaos persists in such case. We also briefly introduce a similar 1D discontinuous mapping based on the rounding function. These alternative systems show significantly smaller regions of robust chaos and greater susceptibility to periodic windows. Finally, we have explored various types of spatiotemporal patterns observed in the ring-star network configuration including synchronized state, cluster synchronization, and cluster chimera state. To understand the transition of various spatiotemporal patterns with simultaneous variations of the ring and star coupling strengths, we computed a two-parameter regime map in the coupling strength plane highlighting transitions of various novel spatiotemporal patterns.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117913"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072019","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}
Efficient warning indicator systems demand signals that are unpredictable to prevent habituation. This paper proposes a novel self-sustained chaotic warning indicator system based on a photoresponsive liquid crystal elastomer (LCE) fiber to generate inherently unpredictable optical warning signals. In this system, the displacement of the mass sphere adjusts a sliding rheostat to change the illumination intensity, which in turn affects the displacement of the mass sphere. This study establishes a theoretical model coupling LCE photodynamics with mechanical oscillation. Numerical simulation reveals two autonomous motion modes crucial: self-sustained periodic oscillation and self-sustained chaotic motion. The periodic mode arises from a precise energy balance between photoinduced contraction and damping, suitable for rhythmic alerts. In contrast, the chaotic mode stems from a persistent temporal energy imbalance, producing the unpredictable signals for urgent or anti-habituation alerts. Through the bifurcation diagram and comprehensive parameter analysis, the transformation relationships among these modes are plotted. The chaotic warning indicator system generates chaotic warning signals through an inherent optomechanical feedback loop, breaking through the traditional warning system that usually uses periodic signals for warning and significantly improving the warning effect. This work provides a theoretical basis for designing controllable, chaotic warning indicator system and demonstrates the potential of the nonlinear system based on LCE in dynamic security alerts and soft robot applications.
{"title":"Self-sustained chaotic warning indicator system based on liquid crystal elastomer","authors":"Peibao Xu , Hongwei Zhu , Kuan Zhou , Xueli Ren , Lin Zhou","doi":"10.1016/j.chaos.2026.117984","DOIUrl":"10.1016/j.chaos.2026.117984","url":null,"abstract":"<div><div>Efficient warning indicator systems demand signals that are unpredictable to prevent habituation. This paper proposes a novel self-sustained chaotic warning indicator system based on a photoresponsive liquid crystal elastomer (LCE) fiber to generate inherently unpredictable optical warning signals. In this system, the displacement of the mass sphere adjusts a sliding rheostat to change the illumination intensity, which in turn affects the displacement of the mass sphere. This study establishes a theoretical model coupling LCE photodynamics with mechanical oscillation. Numerical simulation reveals two autonomous motion modes crucial: self-sustained periodic oscillation and self-sustained chaotic motion. The periodic mode arises from a precise energy balance between photoinduced contraction and damping, suitable for rhythmic alerts. In contrast, the chaotic mode stems from a persistent temporal energy imbalance, producing the unpredictable signals for urgent or anti-habituation alerts. Through the bifurcation diagram and comprehensive parameter analysis, the transformation relationships among these modes are plotted. The chaotic warning indicator system generates chaotic warning signals through an inherent optomechanical feedback loop, breaking through the traditional warning system that usually uses periodic signals for warning and significantly improving the warning effect. This work provides a theoretical basis for designing controllable, chaotic warning indicator system and demonstrates the potential of the nonlinear system based on LCE in dynamic security alerts and soft robot applications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117984"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072020","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 : 2026-01-27DOI: 10.1016/j.chaos.2026.117926
Yiqing Li , Yan Liang , Zhenzhou Lu , Fang Yuan , Yujiao Dong , Guangyi Wang , Ahmet Samil Demirkol , Ronald Tetzlaff , Alon Ascoli
Locally active memristors (LAMs) exhibit small-signal amplification capability, making them suitable for use in artificial neuron circuits. Spiking oscillations and chaotic dynamics are two representative neuromorphic behaviors that have shown promise in spiking neural networks and combinatorial optimization applications. Spiking oscillations are identified using a newly proposed criterion based on the signal's rate of change and energy consumption characteristics, while chaotic dynamics are verified through Lyapunov exponent analysis. To investigate their underlying mechanisms, simple second-order and third-order memristive neuron circuits are employed to generate periodic spiking and chaotic neuromorphic behaviors, respectively. Based on nonlinear circuit and dynamics theory as well as numerical analysis methods, the impacts of model expressions and parameters on spiking oscillation and chaotic behavior are quantitatively investigated. The analysis results indicate that the emergence of these two neuromorphic behaviors mainly depends on the expression of memristance/memductance functions in the LAMs polynomial model and the characteristics of the instantaneous resistance and the differential resistance of the LAMs at the operating point. Hardware implementations of both circuits further validate the theoretical and simulation results. This insight provides valuable guidance for designing and optimizing neuron models and neuromorphic computing devices, advancing the realization of circuit-oriented neuromorphic computing systems.
{"title":"Mechanisms investigation of spiking and chaos in memristive neurons based on locally active memristor models","authors":"Yiqing Li , Yan Liang , Zhenzhou Lu , Fang Yuan , Yujiao Dong , Guangyi Wang , Ahmet Samil Demirkol , Ronald Tetzlaff , Alon Ascoli","doi":"10.1016/j.chaos.2026.117926","DOIUrl":"10.1016/j.chaos.2026.117926","url":null,"abstract":"<div><div>Locally active memristors (LAMs) exhibit small-signal amplification capability, making them suitable for use in artificial neuron circuits. Spiking oscillations and chaotic dynamics are two representative neuromorphic behaviors that have shown promise in spiking neural networks and combinatorial optimization applications. Spiking oscillations are identified using a newly proposed criterion based on the signal's rate of change and energy consumption characteristics, while chaotic dynamics are verified through Lyapunov exponent analysis. To investigate their underlying mechanisms, simple second-order and third-order memristive neuron circuits are employed to generate periodic spiking and chaotic neuromorphic behaviors, respectively. Based on nonlinear circuit and dynamics theory as well as numerical analysis methods, the impacts of model expressions and parameters on spiking oscillation and chaotic behavior are quantitatively investigated. The analysis results indicate that the emergence of these two neuromorphic behaviors mainly depends on the expression of memristance/memductance functions in the LAMs polynomial model and the characteristics of the instantaneous resistance and the differential resistance of the LAMs at the operating point. Hardware implementations of both circuits further validate the theoretical and simulation results. This insight provides valuable guidance for designing and optimizing neuron models and neuromorphic computing devices, advancing the realization of circuit-oriented neuromorphic computing systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117926"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072021","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 : 2026-01-27DOI: 10.1016/j.chaos.2026.117977
Qianming Ding , Yipeng Hu , Tianyu Li , Ying Xie , Ya Jia
Optogenetics holds immense potential for modulating arrhythmias, yet its application is constrained by the difficulty in localizing the core of spiral waves, with inadequate optical stimulation often inducing wave breakup. The photon-scanning approach eliminates spiral waves by scanning a light stripe, anchoring the spiral wave core, and guiding the core to drift toward the medium boundary. This novel approach eliminates spiral waves without the need for accurate core localization and tissue properties, thereby overcoming the limitations of conventional approaches. This paper proposes an approach using dynamic learning to optimize photon scanning (DLOPS) through integrating photon scanning with the dynamic learning of synchronization techniques. The DLOPS approach eliminates spiral waves in various tissues by adjusting the illuminated area and intensity to reduce the number of activated LEDs. Simulation results indicate that compared to the original photon scanning approach, the DLOPS approach can reduce optical energy consumption by 50% to 85%. Additionally, we propose a “sandwich scanning approach” under challenging periodic boundary conditions, which successfully suppresses wave diffusion and reduces the energy consumption to levels comparable with those under no-flow boundary conditions. Finally, the DLOPS approach exhibits high robustness even in complex heterogeneous tissues. The DLOPS approach proposed in this paper could provide new insights for future research into arrhythmia treatment, thereby offering a novel low-energy and high-efficiency solution.
{"title":"Spiral wave control via dynamic learning optimized photon scanning approach","authors":"Qianming Ding , Yipeng Hu , Tianyu Li , Ying Xie , Ya Jia","doi":"10.1016/j.chaos.2026.117977","DOIUrl":"10.1016/j.chaos.2026.117977","url":null,"abstract":"<div><div>Optogenetics holds immense potential for modulating arrhythmias, yet its application is constrained by the difficulty in localizing the core of spiral waves, with inadequate optical stimulation often inducing wave breakup. The photon-scanning approach eliminates spiral waves by scanning a light stripe, anchoring the spiral wave core, and guiding the core to drift toward the medium boundary. This novel approach eliminates spiral waves without the need for accurate core localization and tissue properties, thereby overcoming the limitations of conventional approaches. This paper proposes an approach using dynamic learning to optimize photon scanning (DLOPS) through integrating photon scanning with the dynamic learning of synchronization techniques. The DLOPS approach eliminates spiral waves in various tissues by adjusting the illuminated area and intensity to reduce the number of activated LEDs. Simulation results indicate that compared to the original photon scanning approach, the DLOPS approach can reduce optical energy consumption by 50% to 85%. Additionally, we propose a “sandwich scanning approach” under challenging periodic boundary conditions, which successfully suppresses wave diffusion and reduces the energy consumption to levels comparable with those under no-flow boundary conditions. Finally, the DLOPS approach exhibits high robustness even in complex heterogeneous tissues. The DLOPS approach proposed in this paper could provide new insights for future research into arrhythmia treatment, thereby offering a novel low-energy and high-efficiency solution.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117977"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072024","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 : 2026-01-27DOI: 10.1016/j.chaos.2026.117970
Meng Su , Wei Xu
Unmanned Surface Vehicles (USVs) have significantly advanced marine technology, offering substantial potential for various applications. This study introduces an innovative random pursuit-evasion framework for USVs, addressing critical gaps by simultaneously incorporating heading angle constraints and environmental noise. By integrating heading angle limits with Gaussian noise to model environmental uncertainties, we establish a robust analytical foundation for examining pursuit-evasion dynamics across varying group sizes. This framework is based on distinct evasion strategies, including Weighted Collective Avoidance and Nearest-Pursuer Avoidance. Our primary metric, mean capture time (CT), is used to evaluate scenarios with varying numbers of pursuers and a single evader. Through numerical simulations and theoretical analyses, we explore how noise intensities and heading limitations jointly affect CTs and evasion effectiveness. Our findings reveal that both environmental disturbances and kinematic constraints significantly impact the dynamics of pursuit-evasion interactions. This research advances the theoretical understanding of random pursuit-evasion dynamics and provides potential applications for enhancing the operational capabilities of USVs in complex and uncertain maritime environments.
{"title":"Pursuit-evasion dynamics for multi-USV with heading angle limits and random noises","authors":"Meng Su , Wei Xu","doi":"10.1016/j.chaos.2026.117970","DOIUrl":"10.1016/j.chaos.2026.117970","url":null,"abstract":"<div><div>Unmanned Surface Vehicles (USVs) have significantly advanced marine technology, offering substantial potential for various applications. This study introduces an innovative random pursuit-evasion framework for USVs, addressing critical gaps by simultaneously incorporating heading angle constraints and environmental noise. By integrating heading angle limits with Gaussian noise to model environmental uncertainties, we establish a robust analytical foundation for examining pursuit-evasion dynamics across varying group sizes. This framework is based on distinct evasion strategies, including Weighted Collective Avoidance and Nearest-Pursuer Avoidance. Our primary metric, mean capture time (CT), is used to evaluate scenarios with varying numbers of pursuers and a single evader. Through numerical simulations and theoretical analyses, we explore how noise intensities and heading limitations jointly affect CTs and evasion effectiveness. Our findings reveal that both environmental disturbances and kinematic constraints significantly impact the dynamics of pursuit-evasion interactions. This research advances the theoretical understanding of random pursuit-evasion dynamics and provides potential applications for enhancing the operational capabilities of USVs in complex and uncertain maritime environments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117970"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071592","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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