We investigate the effects of aging in the noisy voter model considering that the probability to change states decays algebraically with age , defined as the time elapsed since adopting the current state. We study the complete aging scenario, which incorporates aging to both mechanisms of interaction, herding and idiosyncratic behavior, and compare it with the partial aging case, where aging affects only the herding mechanism. Analytical mean-field equations are derived, finding excellent agreement with agent-based simulations on a complete graph. We observe that complete aging enhances consensus formation, shifting the critical point to higher values compared to the partial aging case. However, when the aging probability decays asymptotically to zero for large , a steady state is not always attained for complete aging.
{"title":"Complete aging in the noisy voter model enhances consensus formation","authors":"Jaume Llabrés , Sara Oliver-Bonafoux , Celia Anteneodo , Raúl Toral","doi":"10.1016/j.chaos.2025.116153","DOIUrl":"10.1016/j.chaos.2025.116153","url":null,"abstract":"<div><div>We investigate the effects of aging in the noisy voter model considering that the probability to change states decays algebraically with age <span><math><mi>τ</mi></math></span>, defined as the time elapsed since adopting the current state. We study the complete aging scenario, which incorporates aging to both mechanisms of interaction, herding and idiosyncratic behavior, and compare it with the partial aging case, where aging affects only the herding mechanism. Analytical mean-field equations are derived, finding excellent agreement with agent-based simulations on a complete graph. We observe that complete aging enhances consensus formation, shifting the critical point to higher values compared to the partial aging case. However, when the aging probability decays asymptotically to zero for large <span><math><mi>τ</mi></math></span>, a steady state is not always attained for complete aging.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116153"},"PeriodicalIF":5.3,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508184","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 : 2025-02-27DOI: 10.1016/j.chaos.2025.116210
Jiafu Liu , Junwei Luo , Lu Liu , Liang Zhang , Ranxi Li , Fan Shen
The paper establishes pitch dynamics of a square multi-body sailcraft with a sliding mass as the attitude control actuator in low Earth orbits experiencing typical torques such as gravitational, atmospheric and solar pressure torques. The dominant and perturbed torques are classified in terms of orbit altitudes. The Melnikov method predicts chaotic pitch motion near separatrices, validated through numerical tools including observing time history of the pitch angle, phase plane, Poincare section and power spectral density. An adaptive time-delayed feedback controller with anti-saturation achieves stabilization of chaotic pitch motion onto periodic orbits through constrained sliding mass positioning ([−1, 1] m) for torque generation propellantlessly. The control strategy incorporates gain adjustment and switched schemes to improve steady-state performance, and meanwhile decreasing both the required control torque and actual required control input null. Numerical simulations validate the developed closed-loop system's capability for propellantless stabilization of chaotic pitch motion across three typical altitudes.
{"title":"Chaotic pitch motion and its stabilization of solar sails subjected to environmental torques in low Earth orbits","authors":"Jiafu Liu , Junwei Luo , Lu Liu , Liang Zhang , Ranxi Li , Fan Shen","doi":"10.1016/j.chaos.2025.116210","DOIUrl":"10.1016/j.chaos.2025.116210","url":null,"abstract":"<div><div>The paper establishes pitch dynamics of a square multi-body sailcraft with a sliding mass as the attitude control actuator in low Earth orbits experiencing typical torques such as gravitational, atmospheric and solar pressure torques. The dominant and perturbed torques are classified in terms of orbit altitudes. The Melnikov method predicts chaotic pitch motion near separatrices, validated through numerical tools including observing time history of the pitch angle, phase plane, Poincare section and power spectral density. An adaptive time-delayed feedback controller with anti-saturation achieves stabilization of chaotic pitch motion onto periodic orbits through constrained sliding mass positioning ([−1, 1] m) for torque generation propellantlessly. The control strategy incorporates gain adjustment and switched schemes to improve steady-state performance, and meanwhile decreasing both the required control torque and actual required control input null. Numerical simulations validate the developed closed-loop system's capability for propellantless stabilization of chaotic pitch motion across three typical altitudes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116210"},"PeriodicalIF":5.3,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511410","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 : 2025-02-26DOI: 10.1016/j.chaos.2025.116165
Jiaying Lin , Pinduo Long , Jinfeng Liang , Qionglin Dai , Haihong Li , Junzhong Yang
This study explores the emergence and maintenance of cooperation in evolutionary game theory by incorporating occasional social interactions into Q-learning algorithms. We model the dynamics on a square lattice, where individuals play the Prisoner’s Dilemma Game and update their strategies based on Q-learning and infrequent social interactions. Our main findings reveal a non-monotonic relationship between the game parameter and cooperation levels, with cooperation re-emerging in adverse conditions. The interplay between Q-learning and social learning mechanisms is key, with social learning playing a more significant role in sustaining cooperation under challenging conditions. This work advances our understanding of cooperation maintenance in populations and has implications for designing strategies to foster cooperation in real-world scenarios.
{"title":"The coevolution of cooperation: Integrating Q-learning and occasional social interactions in evolutionary games","authors":"Jiaying Lin , Pinduo Long , Jinfeng Liang , Qionglin Dai , Haihong Li , Junzhong Yang","doi":"10.1016/j.chaos.2025.116165","DOIUrl":"10.1016/j.chaos.2025.116165","url":null,"abstract":"<div><div>This study explores the emergence and maintenance of cooperation in evolutionary game theory by incorporating occasional social interactions into Q-learning algorithms. We model the dynamics on a square lattice, where individuals play the Prisoner’s Dilemma Game and update their strategies based on Q-learning and infrequent social interactions. Our main findings reveal a non-monotonic relationship between the game parameter <span><math><mi>c</mi></math></span> and cooperation levels, with cooperation re-emerging in adverse conditions. The interplay between Q-learning and social learning mechanisms is key, with social learning playing a more significant role in sustaining cooperation under challenging conditions. This work advances our understanding of cooperation maintenance in populations and has implications for designing strategies to foster cooperation in real-world scenarios.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116165"},"PeriodicalIF":5.3,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488484","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 : 2025-02-26DOI: 10.1016/j.chaos.2025.116161
Wen Bao , Rui Xing , Hai-Yan Wang , Jing-Dong Bao
We investigate nonequilibrium physical processes governed by a combination of non-Stokesian friction and nonlinear binding, within a framework where the fluctuation–dissipation theorem remains valid. Two distinct models are examined: a non-stationary Langevin equation and a system exhibiting non-Markovian dynamics, the both can induce the limitation of thermal diffusion: ballistic diffusion. In the first case, this behavior arises when the friction decays inversely with time, while in the second case, it results from a lack of low-frequency components in the driving noise. Then, we demonstrate that a logarithmic potential, acting as a weak binding force, can transition ballistic diffusion into full-scale anomalous diffusion. The effective temperature of the system deviates from the equilibrium value and exhibits nonmonotonic variation with the depth of the potential. Moreover, we study the noise-enhanced stability effect of the metastable state. This work highlights the critical impact of ergodicity breaking and underscores the peculiar role of nonlinear potentials in shaping dynamical behavior.
{"title":"Anomalous diffusion induced by combining non-Stokesian friction with nonlinear binding","authors":"Wen Bao , Rui Xing , Hai-Yan Wang , Jing-Dong Bao","doi":"10.1016/j.chaos.2025.116161","DOIUrl":"10.1016/j.chaos.2025.116161","url":null,"abstract":"<div><div>We investigate nonequilibrium physical processes governed by a combination of non-Stokesian friction and nonlinear binding, within a framework where the fluctuation–dissipation theorem remains valid. Two distinct models are examined: a non-stationary Langevin equation and a system exhibiting non-Markovian dynamics, the both can induce the limitation of thermal diffusion: ballistic diffusion. In the first case, this behavior arises when the friction decays inversely with time, while in the second case, it results from a lack of low-frequency components in the driving noise. Then, we demonstrate that a logarithmic potential, acting as a weak binding force, can transition ballistic diffusion into full-scale anomalous diffusion. The effective temperature of the system deviates from the equilibrium value and exhibits nonmonotonic variation with the depth of the potential. Moreover, we study the noise-enhanced stability effect of the metastable state. This work highlights the critical impact of ergodicity breaking and underscores the peculiar role of nonlinear potentials in shaping dynamical behavior.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116161"},"PeriodicalIF":5.3,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-26DOI: 10.1016/j.chaos.2025.116102
Xianghua Li , Min Teng , Shihong Jiang , Zhen Han , Chao Gao , Vladimir Nekorkin , Petia Radeva
Accurate identification of critical stations is essential for urban public transport networks (UPTNs). However, existing methods mainly focus on the static network structure and single transport systems, limiting their capacity to accurately capture the time-varying importance of stations. To address the limitation, this paper proposes a new method named dynamic station-line centrality (DSLC) to accurately identify the critical stations within bus-metro networks. Initially, this paper constructs a bus-metro load network (BMN) model to address the interaction between bus and metro systems. BMN can effectively reveal the connection tightness between stations, track transfers between different systems, and monitor dynamic passenger flows. Subsequently, we propose DSLC to accurately assess and quantify the time-varying importance of stations. Specifically, a topology enhancement strategy leveraging dynamic passenger flows and community structures is proposed to enhance the topology characteristics of nodes with great passenger flow significance, while overcoming the reliance on time-consuming shortest path algorithms. Additionally, DSLC addresses the identification of time-varying node importance by integrating the reinforcing relationship between stations and server lines. Extensive experiments on a public dataset of Shanghai BMN and comparison to the state-of-the-art methods validate the effectiveness of DSLC in enhancing the robustness and mitigating the propagation of cascading failures. Moreover, DSLC achieves an average improvement of 25.54% in passenger flow loss compared to the suboptimal algorithms, providing valuable insights for traffic managers.
{"title":"A dynamic station-line centrality for identifying critical stations in bus-metro networks","authors":"Xianghua Li , Min Teng , Shihong Jiang , Zhen Han , Chao Gao , Vladimir Nekorkin , Petia Radeva","doi":"10.1016/j.chaos.2025.116102","DOIUrl":"10.1016/j.chaos.2025.116102","url":null,"abstract":"<div><div>Accurate identification of critical stations is essential for urban public transport networks (UPTNs). However, existing methods mainly focus on the static network structure and single transport systems, limiting their capacity to accurately capture the time-varying importance of stations. To address the limitation, this paper proposes a new method named dynamic station-line centrality (DSLC) to accurately identify the critical stations within bus-metro networks. Initially, this paper constructs a bus-metro load network (BMN) model to address the interaction between bus and metro systems. BMN can effectively reveal the connection tightness between stations, track transfers between different systems, and monitor dynamic passenger flows. Subsequently, we propose DSLC to accurately assess and quantify the time-varying importance of stations. Specifically, a topology enhancement strategy leveraging dynamic passenger flows and community structures is proposed to enhance the topology characteristics of nodes with great passenger flow significance, while overcoming the reliance on time-consuming shortest path algorithms. Additionally, DSLC addresses the identification of time-varying node importance by integrating the reinforcing relationship between stations and server lines. Extensive experiments on a public dataset of Shanghai BMN and comparison to the state-of-the-art methods validate the effectiveness of DSLC in enhancing the robustness and mitigating the propagation of cascading failures. Moreover, DSLC achieves an average improvement of 25.54% in passenger flow loss compared to the suboptimal algorithms, providing valuable insights for traffic managers.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116102"},"PeriodicalIF":5.3,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488499","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 : 2025-02-25DOI: 10.1016/j.chaos.2025.116151
Aman Ullah , Yahui Meng
Finding influential nodes is essential for understanding the structure of complex networks and optimizing the dissemination of critical information. The key challenge lies in determining which nodes hold the most significance and how to identify and select a group of disseminators to maximize their influence. Therefore, researchers have proposed various approaches and centrality measures, each offering unique perspectives based on the network’s topology. However, existing methods encounter inherent issues due to their sole consideration of node topology information. They also overlook the interconnectedness between nodes during the node filtering process, leading to imprecise evaluation results and limitations in terms of spread scale. In this paper, we introduce a novel scheme to tackle this problem in the context of social complex networks, termed graph embedding-based hybrid centrality (GEHC). Our proposed GEHC scheme starts by employing the DeepWalk graph embedding method to project the high-dimensional complex graph into a simpler, low-dimensional vector space. This mapping enables efficient calculation of the Euclidean distance between local pairs of nodes, allowing us to capture the proximity of nodes accurately. To further enhance the identification of influential nodes, we integrate network topology information and hybrid centrality indices. To evaluate the performance of our approach, we conduct extensive experiments on real-life networks using standard evaluation metrics. Experimental results on real-world networks demonstrate that our proposed scheme achieves a Kendall rank correlation coefficient close to 0.9, reflecting a strong correlation with the outcomes of the susceptible–infected–recovered model and validating its effectiveness in identifying influential nodes. The experimental results showcase the superiority of our approach in accurately identifying nodes with high influence, surpassing the performance of traditional and recent methods in complex networks.
{"title":"Finding influential nodes via graph embedding and hybrid centrality in complex networks","authors":"Aman Ullah , Yahui Meng","doi":"10.1016/j.chaos.2025.116151","DOIUrl":"10.1016/j.chaos.2025.116151","url":null,"abstract":"<div><div>Finding influential nodes is essential for understanding the structure of complex networks and optimizing the dissemination of critical information. The key challenge lies in determining which nodes hold the most significance and how to identify and select a group of disseminators to maximize their influence. Therefore, researchers have proposed various approaches and centrality measures, each offering unique perspectives based on the network’s topology. However, existing methods encounter inherent issues due to their sole consideration of node topology information. They also overlook the interconnectedness between nodes during the node filtering process, leading to imprecise evaluation results and limitations in terms of spread scale. In this paper, we introduce a novel scheme to tackle this problem in the context of social complex networks, termed graph embedding-based hybrid centrality (GEHC). Our proposed GEHC scheme starts by employing the DeepWalk graph embedding method to project the high-dimensional complex graph into a simpler, low-dimensional vector space. This mapping enables efficient calculation of the Euclidean distance between local pairs of nodes, allowing us to capture the proximity of nodes accurately. To further enhance the identification of influential nodes, we integrate network topology information and hybrid centrality indices. To evaluate the performance of our approach, we conduct extensive experiments on real-life networks using standard evaluation metrics. Experimental results on real-world networks demonstrate that our proposed scheme achieves a Kendall rank correlation coefficient close to 0.9, reflecting a strong correlation with the outcomes of the susceptible–infected–recovered model and validating its effectiveness in identifying influential nodes. The experimental results showcase the superiority of our approach in accurately identifying nodes with high influence, surpassing the performance of traditional and recent methods in complex networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116151"},"PeriodicalIF":5.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480751","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 : 2025-02-25DOI: 10.1016/j.chaos.2025.116160
Jing-jing Liao , Qi Kang , Jia-le Wu , Meng-meng Su , Ting Zhu
The transport of the obstacle lattice with topographic gradients in the direction within a two-dimensional channel is numerically studied under the influence of chiral active particles. The asymmetry of the obstacle lattice and the chirality of the active particles result in directional transport of the obstacle lattice along the longitudinal direction. The obstacle lattice and the chiral active particles move in opposite directions, with their transport direction governed by the chirality of the active particles. The average velocity magnitudes of the chiral active particles and the obstacle lattice exhibit similar trends concerning angular velocity, self-propulsion speed, translational and rotational diffusion coefficient. However, distinct behaviors emerge as the numbers of obstacle particles and active particles vary. Notably, the ratio of the average velocity magnitude of obstacle particles to that of active particles equals the ratio of active particles to obstacle particles. These findings offer insights for the design of advanced smart materials and the development of targeted drug delivery systems.
{"title":"Transport of the obstacle lattice with topographical gradients driven by chiral active particles","authors":"Jing-jing Liao , Qi Kang , Jia-le Wu , Meng-meng Su , Ting Zhu","doi":"10.1016/j.chaos.2025.116160","DOIUrl":"10.1016/j.chaos.2025.116160","url":null,"abstract":"<div><div>The transport of the obstacle lattice with topographic gradients in the <span><math><mi>y</mi></math></span> direction within a two-dimensional channel is numerically studied under the influence of chiral active particles. The asymmetry of the obstacle lattice and the chirality of the active particles result in directional transport of the obstacle lattice along the longitudinal direction. The obstacle lattice and the chiral active particles move in opposite directions, with their transport direction governed by the chirality of the active particles. The average velocity magnitudes of the chiral active particles and the obstacle lattice exhibit similar trends concerning angular velocity, self-propulsion speed, translational and rotational diffusion coefficient. However, distinct behaviors emerge as the numbers of obstacle particles and active particles vary. Notably, the ratio of the average velocity magnitude of obstacle particles to that of active particles equals the ratio of active particles to obstacle particles. These findings offer insights for the design of advanced smart materials and the development of targeted drug delivery systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116160"},"PeriodicalIF":5.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480754","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 : 2025-02-25DOI: 10.1016/j.chaos.2025.116166
Dandan Li , Qiongzi Wu , Dun Han
Based on the prisoner’s dilemma (PD) evolutionary game model and reinforcement learning framework, this paper studies the impact of factors such as temptation payoff, time allocation, and others on agent behavior evolution and strategy selection under limited gaming time resources, across three different agent relationship structures. The results show that an increase in the agent’s gaming time resources and lower temptation payoffs, or the agent’s greater emphasis on long-term rewards and avoidance of excessive behavioral adjustments, all contribute to promoting cooperation between agents. Additionally, the total remaining gaming time between agents gradually increases as the game progresses, while the total gaming time between agents gradually decreases. Both will eventually reach a steady state after a sufficiently large number of game rounds. Further results indicate that an increase in temptation payoff leads to an increase in total remaining gaming time, while reducing the total gaming time between agents. Finally, the measure of heterogeneity in gaming time distribution between agents gradually increases throughout the game process. This is particularly evident when the temptation payoff is high, as the differences in gaming time allocation between agents increase, significantly enhancing the heterogeneity of gaming time among agents in the system. This study provides important theoretical support for understanding agent behavior evolution under limited gaming time resources, especially in dynamic cooperative and competitive game scenarios.
{"title":"On evolution of agent behavior under limited gaming time with reinforcement learning","authors":"Dandan Li , Qiongzi Wu , Dun Han","doi":"10.1016/j.chaos.2025.116166","DOIUrl":"10.1016/j.chaos.2025.116166","url":null,"abstract":"<div><div>Based on the prisoner’s dilemma (PD) evolutionary game model and reinforcement learning framework, this paper studies the impact of factors such as temptation payoff, time allocation, and others on agent behavior evolution and strategy selection under limited gaming time resources, across three different agent relationship structures. The results show that an increase in the agent’s gaming time resources and lower temptation payoffs, or the agent’s greater emphasis on long-term rewards and avoidance of excessive behavioral adjustments, all contribute to promoting cooperation between agents. Additionally, the total remaining gaming time between agents gradually increases as the game progresses, while the total gaming time between agents gradually decreases. Both will eventually reach a steady state after a sufficiently large number of game rounds. Further results indicate that an increase in temptation payoff leads to an increase in total remaining gaming time, while reducing the total gaming time between agents. Finally, the measure of heterogeneity in gaming time distribution between agents gradually increases throughout the game process. This is particularly evident when the temptation payoff is high, as the differences in gaming time allocation between agents increase, significantly enhancing the heterogeneity of gaming time among agents in the system. This study provides important theoretical support for understanding agent behavior evolution under limited gaming time resources, especially in dynamic cooperative and competitive game scenarios.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116166"},"PeriodicalIF":5.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480753","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 : 2025-02-25DOI: 10.1016/j.chaos.2025.116144
Bharathi G.S., Sagithya Thirumalai
Smoking is one of the leading causes of health problems and remains one of the world’s most pressing public health challenges. This paper proposes a modified smoking model based on the Caputo fractional derivative, which turns out to be a system of five nonlinear differential equations. The study employs a dual approach, combining both theoretical and numerical perspectives to analyze the smoking model. In this paper, the existence and uniqueness of the solution are established using fixed-point theory and the Picard–Lindelöf method and the stability for both smoke-free and smoke-present equilibria are analyzed using both Jacobian matrix and Lyapunov functions. Moreover, the model is examined using the spectral collocation method, employing Chebyshev polynomials as basis functions. The convergence and stability of the numerical solutions are captured via the maximum residual error for both integer and fractional orders over different sets of collocation points. The study also examines the effects of different parameters for various fractional order values. Furthermore, the combined effects of the transmission rates, as well as their interactions with recovery, depart, and death rates due to smoking/ingestion, are explored. These results are represented in the form of tables and detailed graphs.
{"title":"Numerical simulation of the smoking model using spectral collocation method","authors":"Bharathi G.S., Sagithya Thirumalai","doi":"10.1016/j.chaos.2025.116144","DOIUrl":"10.1016/j.chaos.2025.116144","url":null,"abstract":"<div><div>Smoking is one of the leading causes of health problems and remains one of the world’s most pressing public health challenges. This paper proposes a modified smoking model based on the Caputo fractional derivative, which turns out to be a system of five nonlinear differential equations. The study employs a dual approach, combining both theoretical and numerical perspectives to analyze the smoking model. In this paper, the existence and uniqueness of the solution are established using fixed-point theory and the Picard–Lindelöf method and the stability for both smoke-free and smoke-present equilibria are analyzed using both Jacobian matrix and Lyapunov functions. Moreover, the model is examined using the spectral collocation method, employing Chebyshev polynomials as basis functions. The convergence and stability of the numerical solutions are captured via the maximum residual error for both integer and fractional orders over different sets of collocation points. The study also examines the effects of different parameters for various fractional order values. Furthermore, the combined effects of the transmission rates, as well as their interactions with recovery, depart, and death rates due to smoking/ingestion, are explored. These results are represented in the form of tables and detailed graphs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116144"},"PeriodicalIF":5.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488498","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 : 2025-02-25DOI: 10.1016/j.chaos.2025.116159
Santana Mondal, Subhas Khajanchi
We develop and analyze a prey–predator interaction model with aposematic prey. Prey’s per-capita growth is subjected to Shepherd’s recruitment function, while predators have a Holling type-II functional response. Ecological dynamics is investigated in presence of a trade-off between prey’s aposematic behavior and resource searching efficiency; significance of the searching efficiency and the saturation constant in the coexistence of prey and predators are explored. Adaptive dynamics is employed to explore the evolution of aposematic behavior of prey species. To assess the evolutionary process, invasion fitness is constructed, and the corresponding evolutionary singular strategies are identified in pairwise invasibility plot (PIP). We discover that the prey strategy evolution is incapable of facilitating evolutionary branching and thus prey species stay monomorphic throughout its evolutionary history. Evolutionary bistability arises when the aposematism function is regarded as normal distribution. Furthermore, predator behavior determines the extent of the feasible evolution set, which in turn dictates the occurrence of bifurcation. For concave–convex–concave form of aposematism function, unique evolutionary attractor is identified. The prey’s aposematic behavior in this situation increases and finally saturates as the prey’s searching efficiency and saturation constant increase.
{"title":"Adaptive evolution of aposematism of a prey species subject to Shepherd’s recruitment function","authors":"Santana Mondal, Subhas Khajanchi","doi":"10.1016/j.chaos.2025.116159","DOIUrl":"10.1016/j.chaos.2025.116159","url":null,"abstract":"<div><div>We develop and analyze a prey–predator interaction model with aposematic prey. Prey’s per-capita growth is subjected to Shepherd’s recruitment function, while predators have a Holling type-II functional response. Ecological dynamics is investigated in presence of a trade-off between prey’s aposematic behavior and resource searching efficiency; significance of the searching efficiency and the saturation constant in the coexistence of prey and predators are explored. Adaptive dynamics is employed to explore the evolution of aposematic behavior of prey species. To assess the evolutionary process, invasion fitness is constructed, and the corresponding evolutionary singular strategies are identified in pairwise invasibility plot (PIP). We discover that the prey strategy evolution is incapable of facilitating evolutionary branching and thus prey species stay monomorphic throughout its evolutionary history. Evolutionary bistability arises when the aposematism function is regarded as normal distribution. Furthermore, predator behavior determines the extent of the feasible evolution set, which in turn dictates the occurrence of bifurcation. For concave–convex–concave form of aposematism function, unique evolutionary attractor is identified. The prey’s aposematic behavior in this situation increases and finally saturates as the prey’s searching efficiency and saturation constant increase.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116159"},"PeriodicalIF":5.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480752","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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