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}
This paper presents a self-contained exposition of the geometric and probabilistic structure of the uniform distribution on the unit sphere . Relying only on spherical coordinates, symmetry principles and basic calculus, we derive fundamental properties of the uniform measure including the distributions of latitude, geodesic angles, spherical distances, Euclidean distances, spherical caps and dot products. The paper further develops explicit formulas for expectations of rotationally symmetric functions and provides closed-form expressions for mean geodesic quantities that arise naturally in geometric probability and quantization theory. In addition, we explain how rotational invariance simplifies spherical integration and leads to transparent interpretations of one-mean and multi-mean geodesic quantization on . The presentation is designed to be accessible to students and researchers seeking an elementary yet rigorous introduction to spherical probability laying a foundation for further study in geometric analysis, directional statistics, and quantization on curved surfaces.
{"title":"Geometric and probabilistic structure of the uniform distribution on the sphere S2","authors":"Pavjeet Singh , S.K. Katiyar , Pooja , Lakshmi Roychowdhury","doi":"10.1016/j.chaos.2025.117771","DOIUrl":"10.1016/j.chaos.2025.117771","url":null,"abstract":"<div><div>This paper presents a self-contained exposition of the geometric and probabilistic structure of the uniform distribution on the unit sphere <span><math><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>. Relying only on spherical coordinates, symmetry principles and basic calculus, we derive fundamental properties of the uniform measure including the distributions of latitude, geodesic angles, spherical distances, Euclidean distances, spherical caps and dot products. The paper further develops explicit formulas for expectations of rotationally symmetric functions and provides closed-form expressions for mean geodesic quantities that arise naturally in geometric probability and quantization theory. In addition, we explain how rotational invariance simplifies spherical integration and leads to transparent interpretations of one-mean and multi-mean geodesic quantization on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. The presentation is designed to be accessible to students and researchers seeking an elementary yet rigorous introduction to spherical probability laying a foundation for further study in geometric analysis, directional statistics, and quantization on curved surfaces.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117771"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072023","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.2026.117923
Hang Ren , Ying Yang , Yu Jiang , He Cao , Jiachen Wang , Fanlong Dong , Geguo Du , Junle Qu , Xueming Liu , Tengfei Wu , Shuangchen Ruan , Chunyu Guo
Period doubling bifurcation (PDB), a universal phenomenon in nonlinear systems, provides a unique perspective for understanding the properties of nonlinear systems, possessing potential important applications. Although it has been intensively investigated in the near-infrared (NIR) spectral region, there are no relevant reports in the mid-infrared (MIR) spectral region. Here, by combined use of numerical analysis and experimental demonstration, the phenomenon of PDB from a fluoride fiber oscillator mode-locked by the nonlinear polarization evolution (NPE) technique is reported for the first time, to the best of our knowledge. In the numerical simulations, the phenomenon of PDB at 2.8 μm is unveiled and analyzed by solving the extended coupled nonlinear Schrödinger equations, in which the pump strength and polarization state are found to play a vital role. A soliton regime with a pulse duration of 309 fs, a repetition rate of 67.16 MHz and an average output power of 63 mW is experimentally achieved, presenting uniform pulse intensity. Based on the simulations, through improving the pump strength, a stable soliton pulse train with the period-doubled state is obtained. This work promotes the development of mid-infrared ultrafast fiber lasers, opening up new opportunities for the MIR optical frequency comb and weak signal detection.
{"title":"Generation of period doubled solitons from a mode-locked fluoride fiber laser","authors":"Hang Ren , Ying Yang , Yu Jiang , He Cao , Jiachen Wang , Fanlong Dong , Geguo Du , Junle Qu , Xueming Liu , Tengfei Wu , Shuangchen Ruan , Chunyu Guo","doi":"10.1016/j.chaos.2026.117923","DOIUrl":"10.1016/j.chaos.2026.117923","url":null,"abstract":"<div><div>Period doubling bifurcation (PDB), a universal phenomenon in nonlinear systems, provides a unique perspective for understanding the properties of nonlinear systems, possessing potential important applications. Although it has been intensively investigated in the near-infrared (NIR) spectral region, there are no relevant reports in the mid-infrared (MIR) spectral region. Here, by combined use of numerical analysis and experimental demonstration, the phenomenon of PDB from a fluoride fiber oscillator mode-locked by the nonlinear polarization evolution (NPE) technique is reported for the first time, to the best of our knowledge. In the numerical simulations, the phenomenon of PDB at 2.8 μm is unveiled and analyzed by solving the extended coupled nonlinear Schrödinger equations, in which the pump strength and polarization state are found to play a vital role. A soliton regime with a pulse duration of 309 fs, a repetition rate of 67.16 MHz and an average output power of 63 mW is experimentally achieved, presenting uniform pulse intensity. Based on the simulations, through improving the pump strength, a stable soliton pulse train with the period-doubled state is obtained. This work promotes the development of mid-infrared ultrafast fiber lasers, opening up new opportunities for the MIR optical frequency comb and weak signal detection.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"206 ","pages":"Article 117923"},"PeriodicalIF":5.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071520","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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