Pub Date : 2025-02-01DOI: 10.1016/j.chaos.2024.115885
Anatoliy A. Pogorui , Ramón M. Rodríguez-Dagnino
This paper deals with a system of interacting telegraph particles starting with different positions on a straight line. It is well-known that the instant of the first collision of two telegraph particle, that starts from different points on a line, has an infinite expectation. Our goal is to find a sufficient number of particles of the system such that the minimum of the first collision instants for these particles has finite th order moments. In particular, finite expectation, finite variance, etc. However, the distribution of this minimum depends on first collisions of all pairs of adjacent particles, and these collisions are dependent random variables, which introduces some difficulties in the analysis.
{"title":"System of telegraph particles with finite moments of the first collision instant of particles","authors":"Anatoliy A. Pogorui , Ramón M. Rodríguez-Dagnino","doi":"10.1016/j.chaos.2024.115885","DOIUrl":"10.1016/j.chaos.2024.115885","url":null,"abstract":"<div><div>This paper deals with a system of interacting telegraph particles starting with different positions on a straight line. It is well-known that the instant of the first collision of two telegraph particle, that starts from different points on a line, has an infinite expectation. Our goal is to find a sufficient number of particles of the system such that the minimum of the first collision instants for these particles has finite <span><math><mi>n</mi></math></span>th order moments. In particular, finite expectation, finite variance, etc. However, the distribution of this minimum depends on first collisions of all pairs of adjacent particles, and these collisions are dependent random variables, which introduces some difficulties in the analysis.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115885"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815840","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115889
Jiakai Lu, Fuhong Min, Linghu Gan, Songtao Yang
As the fundamental unit of the nervous system, neuron is essential for transmitting and processing information, playing a critical role in brain activity regulation. This article develops an electrically coupled Hindmarsh-Rose (HR) neurons incorporating external stimuli to simulate biological neuronal behavior. The bifurcation plot with varying the coupling strength of the system are analyzed through the discrete mapping method, in which period-doubling bifurcations and saddle bifurcation are obtained. The evolutions of period-1 to period-8 and period-3 to period-6 are predicted with stable and unstable periodic orbits, and multiple firing behaviors of such a neuron network are studied using Lyapunov exponent and timing-phase diagram. The real part and magnitudes of eigenvalues with varying the coupling strength for different periodic motions are also plotted to illustrate the bifurcation mechanism of the coupled HR neurons. Moreover, theoretical analysis is validated through FPGA technology, which also accelerates computation and minimizes data storage requirements. Ultimately, a uniform linear segmentation algorithm is utilized to construct bifurcation plots of the coupled HR neuron, and experimental results confirm the model's accuracy.
{"title":"Dynamic analysis of coupled Hindmarsh-Rose neurons with enhanced FPGA implementation","authors":"Jiakai Lu, Fuhong Min, Linghu Gan, Songtao Yang","doi":"10.1016/j.chaos.2024.115889","DOIUrl":"10.1016/j.chaos.2024.115889","url":null,"abstract":"<div><div>As the fundamental unit of the nervous system, neuron is essential for transmitting and processing information, playing a critical role in brain activity regulation. This article develops an electrically coupled Hindmarsh-Rose (HR) neurons incorporating external stimuli to simulate biological neuronal behavior. The bifurcation plot with varying the coupling strength of the system are analyzed through the discrete mapping method, in which period-doubling bifurcations and saddle bifurcation are obtained. The evolutions of period-1 to period-8 and period-3 to period-6 are predicted with stable and unstable periodic orbits, and multiple firing behaviors of such a neuron network are studied using Lyapunov exponent and timing-phase diagram. The real part and magnitudes of eigenvalues with varying the coupling strength for different periodic motions are also plotted to illustrate the bifurcation mechanism of the coupled HR neurons. Moreover, theoretical analysis is validated through FPGA technology, which also accelerates computation and minimizes data storage requirements. Ultimately, a uniform linear segmentation algorithm is utilized to construct bifurcation plots of the coupled HR neuron, and experimental results confirm the model's accuracy.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115889"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815860","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115836
Chi-Fai Lo , Yeontaek Choi , Sergey Nazarenko
We have shown that a stochastic heat engine which is modelled by an over-damped random particle confined in an externally driven time-varying logarithmic-harmonic potential could behave like the wave amplitude of a system of weakly interacting waves. The system of weakly interacting waves may thus serve as an empirical testing ground of the stochastic heat engine. In addition, we have proposed a simple Lie-algebraic method to solve the time evolution equation for the probability density function (p.d.f.) of the system of weakly interacting waves by exploiting its dynamical symmetry. This Lie-algebraic approach has the advantage of generating both the p.d.f. and the generating function in a straightforward manner.
{"title":"Stochastic heat engine acting like a weakly nonlinear wave ensemble","authors":"Chi-Fai Lo , Yeontaek Choi , Sergey Nazarenko","doi":"10.1016/j.chaos.2024.115836","DOIUrl":"10.1016/j.chaos.2024.115836","url":null,"abstract":"<div><div>We have shown that a stochastic heat engine which is modelled by an over-damped random particle confined in an externally driven time-varying logarithmic-harmonic potential could behave like the wave amplitude of a system of weakly interacting waves. The system of weakly interacting waves may thus serve as an empirical testing ground of the stochastic heat engine. In addition, we have proposed a simple Lie-algebraic method to solve the time evolution equation for the probability density function (p.d.f.) of the system of weakly interacting waves by exploiting its dynamical symmetry. This Lie-algebraic approach has the advantage of generating both the p.d.f. and the generating function in a straightforward manner.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115836"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815861","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115852
P. Prakash , K.S. Priyendhu , M. Lakshmanan
In this article, we explain the invariant subspace approach for and -dimensional -component nonlinear coupled systems of PDEs with and without time delays under three different time-fractional derivatives. Also, we explain how this method can be used to derive different types of generalized separable solutions for the nonlinear systems mentioned above through the obtained invariant subspaces. More precisely, we show the applicability of this method using the general class of coupled 2-component nonlinear -dimensional reaction-diffusion system under three time-fractional derivatives. Moreover, we provide a detailed description for obtaining the various types of different dimensional invariant linear 2-component subspaces and their solutions for the underlying coupled 2-component nonlinear -dimensional reaction-diffusion system with appropriate initial-boundary conditions under the three time-fractional derivatives known as (a) Riemann–Liouville (RL) fractional derivative, (b) Caputo fractional derivative, and (c) Hilfer fractional derivative, as examples. Furthermore, we observe that the derived separable solutions under three fractional-order derivatives consist of trigonometric, polynomial, exponential, and Mittag–Leffler functions. Additionally, we present a comparative study of the obtained solutions and results of the discussed nonlinear systems under the three considered fractional derivatives through the corresponding two and three-dimensional plots for various values of fractional orders as well as with the existing literature.
{"title":"Generalized separable solutions for (2+1) and (3+1)-dimensional m-component coupled nonlinear systems of PDEs under three different time-fractional derivatives","authors":"P. Prakash , K.S. Priyendhu , M. Lakshmanan","doi":"10.1016/j.chaos.2024.115852","DOIUrl":"10.1016/j.chaos.2024.115852","url":null,"abstract":"<div><div>In this article, we explain the invariant subspace approach for <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional <span><math><mi>m</mi></math></span>-component nonlinear coupled systems of PDEs with and without time delays under three different time-fractional derivatives. Also, we explain how this method can be used to derive different types of generalized separable solutions for the nonlinear systems mentioned above through the obtained invariant subspaces. More precisely, we show the applicability of this method using the general class of coupled 2-component nonlinear <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional reaction-diffusion system under three time-fractional derivatives. Moreover, we provide a detailed description for obtaining the various types of different dimensional invariant linear 2-component subspaces and their solutions for the underlying coupled 2-component nonlinear <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional reaction-diffusion system with appropriate initial-boundary conditions under the three time-fractional derivatives known as (a) Riemann–Liouville (RL) fractional derivative, (b) Caputo fractional derivative, and (c) Hilfer fractional derivative, as examples. Furthermore, we observe that the derived separable solutions under three fractional-order derivatives consist of trigonometric, polynomial, exponential, and Mittag–Leffler functions. Additionally, we present a comparative study of the obtained solutions and results of the discussed nonlinear systems under the three considered fractional derivatives through the corresponding two and three-dimensional plots for various values of fractional orders as well as with the existing literature.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115852"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857708","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115774
Mario I. Molina
We study a one-dimensional split-ring resonator array containing a single linear/nonlinear magnetic impurity where the usual discrete Laplacian is replaced by a fractional one. In the absence of the impurity, the dispersion relation for magnetoinductive waves is obtained in closed form, with a bandwidth that decreases with a decrease in the fractional exponent. Next, by using lattice Green functions, we obtain the bound state energy and its spatial profile, as a function of the impurity strength. We demonstrate that, at large impurity strengths, the bound state energy becomes linear with impurity strength for both linear and nonlinear impurity cases. The transmission of plane waves is computed semi-analytical, showing a qualitative similarity between the linear and nonlinear impurity cases. Finally, we compute the amount of magnetic energy remaining at the impurity site after evolving the system from a completely initially localized condition at the impurity site. For both cases, linear and nonlinear impurities, it is found that for a fixed fractional exponent, there is trapping of magnetic energy, which increases with an increase in impurity strength. The trapping increases with a decreased fractional exponent for a fixed magnetic strength.
{"title":"The fractional nonlinear magnetoinductive impurity","authors":"Mario I. Molina","doi":"10.1016/j.chaos.2024.115774","DOIUrl":"10.1016/j.chaos.2024.115774","url":null,"abstract":"<div><div>We study a one-dimensional split-ring resonator array containing a single linear/nonlinear magnetic impurity where the usual discrete Laplacian is replaced by a fractional one. In the absence of the impurity, the dispersion relation for magnetoinductive waves is obtained in closed form, with a bandwidth that decreases with a decrease in the fractional exponent. Next, by using lattice Green functions, we obtain the bound state energy and its spatial profile, as a function of the impurity strength. We demonstrate that, at large impurity strengths, the bound state energy becomes linear with impurity strength for both linear and nonlinear impurity cases. The transmission of plane waves is computed semi-analytical, showing a qualitative similarity between the linear and nonlinear impurity cases. Finally, we compute the amount of magnetic energy remaining at the impurity site after evolving the system from a completely initially localized condition at the impurity site. For both cases, linear and nonlinear impurities, it is found that for a fixed fractional exponent, there is trapping of magnetic energy, which increases with an increase in impurity strength. The trapping increases with a decreased fractional exponent for a fixed magnetic strength.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115774"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815849","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115894
Léandre Kamdjeu Kengne , Vitrice Ruben Folifack Signing , Davide Rossi Sebastiano , Raoul Blaise Wafo Tekam , Joakim Vianney Ngamsa Tegnitsap , Manyu Zhao , Qingshi Bao , Jacques Kengne , Pedro Antonio Valdes-Sosa , Ludovico Minati
This paper investigates the simplest autonomous chaotic circuit capable of generating extreme events, comprising a DC voltage source, a series resistor, a capacitor, three inductors, and two bipolar transistors. The statistical properties and synchronization of the extreme events generated by the system are characterized using a simplified equation model, realistic SPICE simulations, and experimental circuit measurements. Heavy-tailed amplitude distributions and Poisson-like inter-event intervals are uncovered, confirming the existence and uncorrelated nature of the extreme events generated in this elementary circuit. Furthermore, a regime is identified where the extreme events synchronize significantly more strongly than the underlying lower-amplitude continuous activity that paces the dynamics, and a novel approach to visualize this situation is introduced. By drawing a tentative parallel with the interictal spikes observed in the neuroelectrical recordings of epilepsy patients, the study proposes that the analog chaotic circuit under consideration could, in the future, serve as a physical model for studying epileptic-like dynamics in electronic networks.
{"title":"Simplest transistor-based chaotic circuit with extreme events: Statistical characterization, synchronization, and analogy with interictal spikes","authors":"Léandre Kamdjeu Kengne , Vitrice Ruben Folifack Signing , Davide Rossi Sebastiano , Raoul Blaise Wafo Tekam , Joakim Vianney Ngamsa Tegnitsap , Manyu Zhao , Qingshi Bao , Jacques Kengne , Pedro Antonio Valdes-Sosa , Ludovico Minati","doi":"10.1016/j.chaos.2024.115894","DOIUrl":"10.1016/j.chaos.2024.115894","url":null,"abstract":"<div><div>This paper investigates the simplest autonomous chaotic circuit capable of generating extreme events, comprising a DC voltage source, a series resistor, a capacitor, three inductors, and two bipolar transistors. The statistical properties and synchronization of the extreme events generated by the system are characterized using a simplified equation model, realistic SPICE simulations, and experimental circuit measurements. Heavy-tailed amplitude distributions and Poisson-like inter-event intervals are uncovered, confirming the existence and uncorrelated nature of the extreme events generated in this elementary circuit. Furthermore, a regime is identified where the extreme events synchronize significantly more strongly than the underlying lower-amplitude continuous activity that paces the dynamics, and a novel approach to visualize this situation is introduced. By drawing a tentative parallel with the interictal spikes observed in the neuroelectrical recordings of epilepsy patients, the study proposes that the analog chaotic circuit under consideration could, in the future, serve as a physical model for studying epileptic-like dynamics in electronic networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115894"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887286","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115731
Xiang Xu , Wei Yang , Lingfei Li , Xianqiang Zhu , Junying Cui , Zihan Zhang , Leilei Wu
The topological and dynamical features of complex networks hold abundant information. How to fully utilize this information for more accurate network structure mining is a significant issue. In this paper, we propose a novel method that simultaneously takes into account both network topological and dynamical features via graph convolutional networks (TD-GCN). Specifically, we obtain the topological features of the network by using the second-order adjacency matrix of the complex network, which captures indirect connections between nodes, for a more detailed representation of network structure, and use the SIS model to generate node state data in the complex network as the dynamical features of the network. The network topological and dynamical features are fused through the graph convolutional neural network. To verify the effectiveness and applicability of our method, we conduct extensive experiments on both simulated networks and real-world networks with various network scales. We comprehensively compare the proposed method with other existing methods in the domains of network link prediction and network node ranking learning. The experimental results show that our method can better capture the characteristic information in complex networks and has better performance compared with other methods.
{"title":"TD-GCN: A novel fusion method for network topological and dynamical features","authors":"Xiang Xu , Wei Yang , Lingfei Li , Xianqiang Zhu , Junying Cui , Zihan Zhang , Leilei Wu","doi":"10.1016/j.chaos.2024.115731","DOIUrl":"10.1016/j.chaos.2024.115731","url":null,"abstract":"<div><div>The topological and dynamical features of complex networks hold abundant information. How to fully utilize this information for more accurate network structure mining is a significant issue. In this paper, we propose a novel method that simultaneously takes into account both network topological and dynamical features via graph convolutional networks (TD-GCN). Specifically, we obtain the topological features of the network by using the second-order adjacency matrix of the complex network, which captures indirect connections between nodes, for a more detailed representation of network structure, and use the SIS model to generate node state data in the complex network as the dynamical features of the network. The network topological and dynamical features are fused through the graph convolutional neural network. To verify the effectiveness and applicability of our method, we conduct extensive experiments on both simulated networks and real-world networks with various network scales. We comprehensively compare the proposed method with other existing methods in the domains of network link prediction and network node ranking learning. The experimental results show that our method can better capture the characteristic information in complex networks and has better performance compared with other methods.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115731"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142777505","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115871
Artur C. Fassoni , Denis C. Braga
Chimeric antigen receptor T-cell (CAR-T) therapy is considered a promising cancer treatment. The dynamic response to this therapy can be broadly divided into a short-term phase, ranging from weeks to months, and a long-term phase, ranging from months to years. While the short-term response, encompassing the multiphasic kinetics of CAR-T cells, is better understood, the mechanisms underlying the outcomes of the long-term response, characterized by sustained remission, relapse, or disease progression, remain less understood due to limited clinical data. Here, we analyze the long-term dynamics of a previously validated mathematical model of CAR-T cell therapy. We perform a comprehensive stability and bifurcation analysis, examining model equilibria and their dynamics over the entire parameter space. Our results show that therapy failure results from a combination of insufficient CAR-T cell proliferation and increased tumor immunosuppression. By combining different techniques of nonlinear dynamics, we identify Hopf and Bogdanov–Takens bifurcations, which allow to elucidate the mechanisms behind oscillatory remissions and transitions to tumor escape. In particular, rapid expansion of CAR-T cells leads to oscillatory tumor control, while increased tumor immunosuppression destabilizes these oscillations, resulting in transient remissions followed by relapse. Our study highlights different mathematical tools to study nonlinear models and provides critical insights into the nonlinear dynamics of CAR-T therapy arising from the complex interplay between CAR-T cells and tumor cells.
{"title":"Nonlinear dynamics of CAR-T cell therapy","authors":"Artur C. Fassoni , Denis C. Braga","doi":"10.1016/j.chaos.2024.115871","DOIUrl":"10.1016/j.chaos.2024.115871","url":null,"abstract":"<div><div>Chimeric antigen receptor T-cell (CAR-T) therapy is considered a promising cancer treatment. The dynamic response to this therapy can be broadly divided into a short-term phase, ranging from weeks to months, and a long-term phase, ranging from months to years. While the short-term response, encompassing the multiphasic kinetics of CAR-T cells, is better understood, the mechanisms underlying the outcomes of the long-term response, characterized by sustained remission, relapse, or disease progression, remain less understood due to limited clinical data. Here, we analyze the long-term dynamics of a previously validated mathematical model of CAR-T cell therapy. We perform a comprehensive stability and bifurcation analysis, examining model equilibria and their dynamics over the entire parameter space. Our results show that therapy failure results from a combination of insufficient CAR-T cell proliferation and increased tumor immunosuppression. By combining different techniques of nonlinear dynamics, we identify Hopf and Bogdanov–Takens bifurcations, which allow to elucidate the mechanisms behind oscillatory remissions and transitions to tumor escape. In particular, rapid expansion of CAR-T cells leads to oscillatory tumor control, while increased tumor immunosuppression destabilizes these oscillations, resulting in transient remissions followed by relapse. Our study highlights different mathematical tools to study nonlinear models and provides critical insights into the nonlinear dynamics of CAR-T therapy arising from the complex interplay between CAR-T cells and tumor cells.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115871"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815844","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115794
Yichen Lu , Yixin Xu , Wanrou Cai , Zhuanghe Tian , Jie Xu , Simin Wang , Tong Zhu , Yali Liu , Mengchu Wang , Yilin Zhou , Chengxu Yan , Chenlu Li , Zhigang Zheng
Chiral swarmalators are active particles with intrinsic dynamical chirality that exhibit persistent rotational motion in space. Collaborative spatial swarming behaviors emerge when chiral swarmalators with heterogeneous chiralities are coupled in an alignment rule. In this paper, we extensively studied the self-organized swarming dynamics of populations of spatially non-interacting chiral swarmalators with phase coupling from the viewpoint of nonlinear dynamics and synchronization. Chiral synchronization dynamics plays important role in adapting spatial swarming behaviors. By modulating the coupling strength and scope, swarmalators may organize into coordinated circlings, spatial clusterings, and other swarming patterns. Chirality-induced phase separations of circling and cluster patterns are revealed, which obeys the interesting rule of “like chiralities attract, while opposite chiralities repel”. The formation mechanism and transitions of these various swarming patterns are explored, and the phase diagrams are given. Critical boundaries separating various collective states are analytically derived. These miscellaneous ordered swarming patterns are shown to be robust to parameter heterogeneity and stochastic noises. The present paves an avenue of the pattern formation and swarming dynamics of interacting chiral agents.
{"title":"Self-organized circling, clustering and swarming in populations of chiral swarmalators","authors":"Yichen Lu , Yixin Xu , Wanrou Cai , Zhuanghe Tian , Jie Xu , Simin Wang , Tong Zhu , Yali Liu , Mengchu Wang , Yilin Zhou , Chengxu Yan , Chenlu Li , Zhigang Zheng","doi":"10.1016/j.chaos.2024.115794","DOIUrl":"10.1016/j.chaos.2024.115794","url":null,"abstract":"<div><div>Chiral swarmalators are active particles with intrinsic dynamical chirality that exhibit persistent rotational motion in space. Collaborative spatial swarming behaviors emerge when chiral swarmalators with heterogeneous chiralities are coupled in an alignment rule. In this paper, we extensively studied the self-organized swarming dynamics of populations of spatially non-interacting chiral swarmalators with phase coupling from the viewpoint of nonlinear dynamics and synchronization. Chiral synchronization dynamics plays important role in adapting spatial swarming behaviors. By modulating the coupling strength and scope, swarmalators may organize into coordinated circlings, spatial clusterings, and other swarming patterns. Chirality-induced phase separations of circling and cluster patterns are revealed, which obeys the interesting rule of “like chiralities attract, while opposite chiralities repel”. The formation mechanism and transitions of these various swarming patterns are explored, and the phase diagrams are given. Critical boundaries separating various collective states are analytically derived. These miscellaneous ordered swarming patterns are shown to be robust to parameter heterogeneity and stochastic noises. The present paves an avenue of the pattern formation and swarming dynamics of interacting chiral agents.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115794"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815884","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 work aims to analyze the dynamics of the restricted five-body problem when the primaries are non-spherical spheroids. We explored numerically three different scenarios: (i) when only the main body creates a potential with either oblateness or prolateness effect; (ii) when only peripheral bodies generate potentials with either oblateness or prolateness effects; and (iii) when all the primary bodies create potentials with either oblateness or prolate effects. We conducted a numerical analysis to study the motion of infinitesimal body under the gravitational influence of four non-spherical primaries. In this analysis, we revealed that the oblate or prolate bodies significantly affect the dynamics of the equilibrium points (EPs), their linear stability, and permissible regions of motion. Furthermore, we demonstrate that the total number of EPs depends on the mass parameter, the oblateness and prolateness parameters or the combinations of these parameters. The specific ranges of oblateness or prolateness values where the equilibrium points are linearly stable are also found.
这项研究旨在分析当基体为非球形时受限五体问题的动力学。我们在数值上探索了三种不同情况：(i)当只有主体产生具有扁球形或扁球形效应的势时；(ii)当只有外围体产生具有扁球形或扁球形效应的势时；以及(iii)当所有主体产生具有扁球形或扁球形效应的势时。我们进行了数值分析，研究了无穷小体在四个非球形主天体引力影响下的运动。在分析中，我们发现扁球体或长球体会显著影响平衡点（EP）的动力学、其线性稳定性和允许的运动区域。此外，我们还证明了 EP 的总数取决于质量参数、扁圆度和扁长度参数或这些参数的组合。我们还找到了平衡点线性稳定的扁平率或扁平率值的具体范围。
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