Pub Date : 2024-11-28DOI: 10.1016/j.physd.2024.134453
Tongfei Li , Yao Ge , Fangxia Zhao , Jiancheng Weng , Wenhan Zhou , Songpo Yang
The introduction of ride-sharing services has significantly diversified commuting options for urban residents. In multi-mode cities, residents select travel modes based on their perception of the costs for various available options, while these perceptions are updated daily. As a result, residents’ travel mode choices and mode-split traffic flows vary day by day. To capture the nonlinear evolution phenomenon of their mode choice behaviors and mode-split traffic flows, we focus on a linear monocentric city with the introduction of ride-sharing services and develop a deterministic discrete-time day-to-day dynamic evolution model. Our model incorporates residents’ limited perceptions to better reflect real-world scenarios. Moreover, considering one ride-sharing driver is allowed to pick up multiple passengers, specific constraints on the number of ride-sharing drivers and passengers (i.e., side constraints) are added to the model formulation. Thus, the proposed model is a discrete-time day-to-day dynamic asymmetric stochastic user equilibrium model with side constraints, which have rarely been studied. The uniqueness of optimal Lagrange multipliers corresponding to side constraints in the day-to-day dynamic evolution model is demonstrated, which makes us successfully extend related literature on static ride-sharing equilibrium to the study of dynamic stochastic ride-sharing user equilibrium problems. Furthermore, we consider the stability issue of the equilibrium and provide sufficient and necessary conditions for its asymptotic stability. Finally, numerical examples are conducted to validate the properties and effectiveness of our dynamic model.
{"title":"Day-to-day dynamic traffic evolution in the urban traffic system with ride-sharing","authors":"Tongfei Li , Yao Ge , Fangxia Zhao , Jiancheng Weng , Wenhan Zhou , Songpo Yang","doi":"10.1016/j.physd.2024.134453","DOIUrl":"10.1016/j.physd.2024.134453","url":null,"abstract":"<div><div>The introduction of ride-sharing services has significantly diversified commuting options for urban residents. In multi-mode cities, residents select travel modes based on their perception of the costs for various available options, while these perceptions are updated daily. As a result, residents’ travel mode choices and mode-split traffic flows vary day by day. To capture the nonlinear evolution phenomenon of their mode choice behaviors and mode-split traffic flows, we focus on a linear monocentric city with the introduction of ride-sharing services and develop a deterministic discrete-time day-to-day dynamic evolution model. Our model incorporates residents’ limited perceptions to better reflect real-world scenarios. Moreover, considering one ride-sharing driver is allowed to pick up multiple passengers, specific constraints on the number of ride-sharing drivers and passengers (i.e., side constraints) are added to the model formulation. Thus, the proposed model is a discrete-time day-to-day dynamic asymmetric stochastic user equilibrium model with side constraints, which have rarely been studied. The uniqueness of optimal Lagrange multipliers corresponding to side constraints in the day-to-day dynamic evolution model is demonstrated, which makes us successfully extend related literature on static ride-sharing equilibrium to the study of dynamic stochastic ride-sharing user equilibrium problems. Furthermore, we consider the stability issue of the equilibrium and provide sufficient and necessary conditions for its asymptotic stability. Finally, numerical examples are conducted to validate the properties and effectiveness of our dynamic model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134453"},"PeriodicalIF":2.7,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142756867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.physd.2024.134448
Shanshan Peng, Jianquan Lu
The high-dimensional Kuramoto model (HDKM) on the unit sphere is commonly used to explain the phase synchronization of coupled oscillators in dynamic systems. However, the current model featuring fixed-amplitude oscillators cannot characterize some systems with varying-amplitude oscillators, such as optical arrays, satellite clusters. Herein, an amplitude-dependent HDKM (AHDKM), defined in a linear space rather than on a unit sphere, is first proposed. This model incorporating amplitude dynamics can be reduced to the HDKM for any coupling strength among oscillators. Next, oscillator distributions at equilibrium points are accurately described to facilitate the analysis of the AHDKM convergence. To determine the global attractivity of equilibrium point set, an easily verifiable sufficient criterion is established by a height function constructed at equilibrium points instead of a strict “Lyapunov function”. Based on this criterion, almost global synchronization of the AHDKM is rigorously proved under different connected graphs via the derived instability of non-synchronized equilibrium points. Finally, main theoretical results are verified through numerical simulations.
{"title":"Almost global synchronization of amplitude-dependent high-dimensional Kuramoto model","authors":"Shanshan Peng, Jianquan Lu","doi":"10.1016/j.physd.2024.134448","DOIUrl":"10.1016/j.physd.2024.134448","url":null,"abstract":"<div><div>The high-dimensional Kuramoto model (HDKM) on the unit sphere is commonly used to explain the phase synchronization of coupled oscillators in dynamic systems. However, the current model featuring fixed-amplitude oscillators cannot characterize some systems with varying-amplitude oscillators, such as optical arrays, satellite clusters. Herein, an amplitude-dependent HDKM (AHDKM), defined in a linear space rather than on a unit sphere, is first proposed. This model incorporating amplitude dynamics can be reduced to the HDKM for any coupling strength among oscillators. Next, oscillator distributions at equilibrium points are accurately described to facilitate the analysis of the AHDKM convergence. To determine the global attractivity of equilibrium point set, an easily verifiable sufficient criterion is established by a height function constructed at equilibrium points instead of a strict “Lyapunov function”. Based on this criterion, almost global synchronization of the AHDKM is rigorously proved under different connected graphs via the derived instability of non-synchronized equilibrium points. Finally, main theoretical results are verified through numerical simulations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134448"},"PeriodicalIF":2.7,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.physd.2024.134447
Ru Qu, DongFeng Zhang
<div><div>This paper focuses on the quasi-periodically forced reversible system: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mover><mrow><mi>u</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mtext>i</mtext><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mtext>i</mtext><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><mover><mrow><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mo>−</mo><mtext>i</mtext><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>−</mo><mtext>i</mtext><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span> where the frequency vector <span><math><mrow><mi>ω</mi><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>α</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mi>α</mi></math></span> being an irrational number, and <span><math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>l</mi></mrow></msup><mo>×</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>l</mi></mrow></msup></mrow></math></span>. The matrix <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow></mrow></math></span> is an <span><math><mrow><mi>l</mi><mo>×</mo><mi>l</mi></mrow></math></span> constant matrix that depends only on the parameter <span><math><mi>ξ</mi></math></span>, and <span><math><mi>f</mi></math></span> represents a small perturbation that also depends on <span><math><mi>ξ</mi></math></span> as a parameter. Based on the CD bridge method and the improved KAM iteration with parameters, it is proved that for most of the parameter <span><math><mi>ξ</mi></math></span>, the reversible system can be reduced to the form: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mover><mrow><mi>u</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mtext>i</mtext><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mtext>i</mtext><msub><mrow><mi>V</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mtext>i</mtext><msub><mrow><mi>f</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>,</mo><mi>
{"title":"The existence of invariant tori of reversible systems with Liouvillean frequency and its applications","authors":"Ru Qu, DongFeng Zhang","doi":"10.1016/j.physd.2024.134447","DOIUrl":"10.1016/j.physd.2024.134447","url":null,"abstract":"<div><div>This paper focuses on the quasi-periodically forced reversible system: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mover><mrow><mi>u</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mtext>i</mtext><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mtext>i</mtext><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><mover><mrow><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mo>−</mo><mtext>i</mtext><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>−</mo><mtext>i</mtext><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span> where the frequency vector <span><math><mrow><mi>ω</mi><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>α</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mi>α</mi></math></span> being an irrational number, and <span><math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>l</mi></mrow></msup><mo>×</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>l</mi></mrow></msup></mrow></math></span>. The matrix <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow></mrow></math></span> is an <span><math><mrow><mi>l</mi><mo>×</mo><mi>l</mi></mrow></math></span> constant matrix that depends only on the parameter <span><math><mi>ξ</mi></math></span>, and <span><math><mi>f</mi></math></span> represents a small perturbation that also depends on <span><math><mi>ξ</mi></math></span> as a parameter. Based on the CD bridge method and the improved KAM iteration with parameters, it is proved that for most of the parameter <span><math><mi>ξ</mi></math></span>, the reversible system can be reduced to the form: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mover><mrow><mi>u</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mtext>i</mtext><mi>A</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mtext>i</mtext><msub><mrow><mi>V</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mtext>i</mtext><msub><mrow><mi>f</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mo>¯</mo></mover><mo>,</mo><mi>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134447"},"PeriodicalIF":2.7,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.physd.2024.134437
Hui Zhao , Aidi Liu , Lei Zhou , Sijie Niu , Xizhan Gao , Mingwen Zheng , Xin Li , Lixiang Li
This paper is concerned with the predefined-time modified function projective synchronization problem of memristor-based multidirectional associative memory neural networks (MMAMNNs) with time-varying delay. Firstly, a new predefined-time stability theorem is proposed, which imposes more relaxed and effective conditions on the Lyapunov-Krasovskii function (LKF). Secondly, by designing a new feedback control strategy, sufficient conditions for ensuring the predefined-time modified function projection synchronization between master and slave systems are obtained. In addition, by changing the projection factor, the results of this paper can be flexibly extended to various synchronization types, such as complete synchronization, anti-synchronization, and proportional synchronization. Finally, the correctness of the theory is verified through numerical simulations.
{"title":"Predefined-time modified function projective synchronization of memristor-based multidirectional associative memory neural networks with time-varying delay","authors":"Hui Zhao , Aidi Liu , Lei Zhou , Sijie Niu , Xizhan Gao , Mingwen Zheng , Xin Li , Lixiang Li","doi":"10.1016/j.physd.2024.134437","DOIUrl":"10.1016/j.physd.2024.134437","url":null,"abstract":"<div><div>This paper is concerned with the predefined-time modified function projective synchronization problem of memristor-based multidirectional associative memory neural networks (MMAMNNs) with time-varying delay. Firstly, a new predefined-time stability theorem is proposed, which imposes more relaxed and effective conditions on the Lyapunov-Krasovskii function (LKF). Secondly, by designing a new feedback control strategy, sufficient conditions for ensuring the predefined-time modified function projection synchronization between master and slave systems are obtained. In addition, by changing the projection factor, the results of this paper can be flexibly extended to various synchronization types, such as complete synchronization, anti-synchronization, and proportional synchronization. Finally, the correctness of the theory is verified through numerical simulations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134437"},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.physd.2024.134418
Christian Moya , Amirhossein Mollaali , Zecheng Zhang , Lu Lu , Guang Lin
In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we enhance the uncertainty quantification frameworks (B-DeepONet and Prob-DeepONet) previously proposed by the authors by using split conformal prediction. By combining conformal prediction with our Prob- and B-DeepONets, we effectively quantify uncertainty by generating rigorous prediction intervals for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We refer to this distribution-free effective uncertainty quantification framework as split conformal Quantile-DeepONet regression. Finally, we demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples, and multi-fidelity learning.
{"title":"Conformalized-DeepONet: A distribution-free framework for uncertainty quantification in deep operator networks","authors":"Christian Moya , Amirhossein Mollaali , Zecheng Zhang , Lu Lu , Guang Lin","doi":"10.1016/j.physd.2024.134418","DOIUrl":"10.1016/j.physd.2024.134418","url":null,"abstract":"<div><div>In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we enhance the uncertainty quantification frameworks (B-DeepONet and Prob-DeepONet) previously proposed by the authors by using split conformal prediction. By combining conformal prediction with our Prob- and B-DeepONets, we effectively quantify uncertainty by generating rigorous prediction intervals for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We refer to this distribution-free effective uncertainty quantification framework as split conformal Quantile-DeepONet regression. Finally, we demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples, and multi-fidelity learning.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134418"},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we explore a multilayered structure in which the coupled oscillators of one layer serve as a shared medium for an uncoupled population of neurons. The layers function based on the memristive Rulkov map, and interlayer connections are established through magnetic flux variables, referred to as field coupling. We adopt both hybrid (electrical and chemical) and exclusively chemical couplings for intralayer connectivity. The study highlights the pivotal role of the reversal potential in the dynamics of chemical coupling, while the firing threshold and sigmoid slope play lesser roles. Synchrony analysis reveals distinct synchronization behaviors between the layers. Notably, although the coupled layer can achieve phase synchrony, it fails to induce comparable synchrony in the uncoupled layer. Our findings also highlight the emergence of distinct collective dynamics in the uncoupled network, influenced by the coherence level of the flux variables in the coupled layer. Specifically, incoherent, two-clustered, and globally synchronized oscillations of flux variables in the coupled layer lead to chimera states, two-cluster synchronization, and complete synchronization in the uncoupled neurons, respectively.
{"title":"Multilayer structure-induced collective dynamics in uncoupled memristive Rulkov neurons: Impact of field coupling and intralayer connections","authors":"Deivasundari Muthukumar , Dorsa Nezhad Hajian , Hayder Natiq , Mahtab Mehrabbeik , Nikhil Pal , Sajad Jafari","doi":"10.1016/j.physd.2024.134464","DOIUrl":"10.1016/j.physd.2024.134464","url":null,"abstract":"<div><div>In this study, we explore a multilayered structure in which the coupled oscillators of one layer serve as a shared medium for an uncoupled population of neurons. The layers function based on the memristive Rulkov map, and interlayer connections are established through magnetic flux variables, referred to as field coupling. We adopt both hybrid (electrical and chemical) and exclusively chemical couplings for intralayer connectivity. The study highlights the pivotal role of the reversal potential in the dynamics of chemical coupling, while the firing threshold and sigmoid slope play lesser roles. Synchrony analysis reveals distinct synchronization behaviors between the layers. Notably, although the coupled layer can achieve phase synchrony, it fails to induce comparable synchrony in the uncoupled layer. Our findings also highlight the emergence of distinct collective dynamics in the uncoupled network, influenced by the coherence level of the flux variables in the coupled layer. Specifically, incoherent, two-clustered, and globally synchronized oscillations of flux variables in the coupled layer lead to chimera states, two-cluster synchronization, and complete synchronization in the uncoupled neurons, respectively.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134464"},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.physd.2024.134438
A. Alonso-Izquierdo , D. Miguélez-Caballero , L.M. Nieto
The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions have two shape modes (one longitudinal and one orthogonal to the kink orbit), in addition to the zero mode, and in which energy redistribution can occur among these three discrete modes. We investigate the scattering between wobbling kinks whose orthogonal shape mode is initially excited, examining how the final velocities, amplitudes, and frequencies depend on the initial excitation amplitude. The differences that this model presents with respect to the model and its novel properties are highlighted. This analysis sheds light on the intricate dynamics that arise from the interplay between multiple degrees of freedom in kink scattering processes, offering insights distinct from those observed in simpler models.
{"title":"Scattering between orthogonally wobbling kinks","authors":"A. Alonso-Izquierdo , D. Miguélez-Caballero , L.M. Nieto","doi":"10.1016/j.physd.2024.134438","DOIUrl":"10.1016/j.physd.2024.134438","url":null,"abstract":"<div><div>The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions have two shape modes (one longitudinal and one orthogonal to the kink orbit), in addition to the zero mode, and in which energy redistribution can occur among these three discrete modes. We investigate the scattering between wobbling kinks whose orthogonal shape mode is initially excited, examining how the final velocities, amplitudes, and frequencies depend on the initial excitation amplitude. The differences that this model presents with respect to the <span><math><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> model and its novel properties are highlighted. This analysis sheds light on the intricate dynamics that arise from the interplay between multiple degrees of freedom in kink scattering processes, offering insights distinct from those observed in simpler models.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134438"},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.physd.2024.134446
Mohammad Daneshvar , Richard C. Barnard , Cory Hauck , Ilya Timofeyev
In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. We demonstrate the validity of the closure with numerical simulations.
{"title":"Modeling information flow in a computer processor with a multi-stage queuing model","authors":"Mohammad Daneshvar , Richard C. Barnard , Cory Hauck , Ilya Timofeyev","doi":"10.1016/j.physd.2024.134446","DOIUrl":"10.1016/j.physd.2024.134446","url":null,"abstract":"<div><div>In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. We demonstrate the validity of the closure with numerical simulations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134446"},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.physd.2024.134434
Peng-Fei Han , Wen-Xiu Ma , Ru-Suo Ye , Yi Zhang
The inverse scattering transform for the defocusing–defocusing coupled Hirota equations with non-zero boundary conditions at infinity is thoroughly discussed. We delve into the analytical properties of the Jost eigenfunctions and scrutinize the characteristics of the scattering coefficients. To enhance our investigation of the fundamental eigenfunctions, we have derived additional auxiliary eigenfunctions with the help of the adjoint problem. Two symmetry conditions are studied to constrain the behavior of the eigenfunctions and scattering coefficients. Utilizing these symmetries, we precisely delineate the discrete spectrum and establish the associated symmetries of the scattering data. By framing the inverse problem within the context of the Riemann–Hilbert problem, we develop suitable jump conditions to express the eigenfunctions. Consequently, we have not only derived the pure soliton solutions from the defocusing–defocusing coupled Hirota equations but also provided the multiple double-pole solutions for the first time.
{"title":"Inverse scattering transform for the defocusing–defocusing coupled Hirota equations with non-zero boundary conditions: Multiple double-pole solutions","authors":"Peng-Fei Han , Wen-Xiu Ma , Ru-Suo Ye , Yi Zhang","doi":"10.1016/j.physd.2024.134434","DOIUrl":"10.1016/j.physd.2024.134434","url":null,"abstract":"<div><div>The inverse scattering transform for the defocusing–defocusing coupled Hirota equations with non-zero boundary conditions at infinity is thoroughly discussed. We delve into the analytical properties of the Jost eigenfunctions and scrutinize the characteristics of the scattering coefficients. To enhance our investigation of the fundamental eigenfunctions, we have derived additional auxiliary eigenfunctions with the help of the adjoint problem. Two symmetry conditions are studied to constrain the behavior of the eigenfunctions and scattering coefficients. Utilizing these symmetries, we precisely delineate the discrete spectrum and establish the associated symmetries of the scattering data. By framing the inverse problem within the context of the Riemann–Hilbert problem, we develop suitable jump conditions to express the eigenfunctions. Consequently, we have not only derived the pure soliton solutions from the defocusing–defocusing coupled Hirota equations but also provided the multiple double-pole solutions for the first time.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134434"},"PeriodicalIF":2.7,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-21DOI: 10.1016/j.physd.2024.134430
Kota Ikeda , Toru Kan , Toshiyuki Ogawa
In traffic flow theory, hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level car-following models. Self-organized wave propagation, which characterizes congestion, has been replicated in these macroscopic models. However, the existence of wave propagation has only been validated using numerical technique or formal analyses and has not yet been rigorously proven. Therefore, analytical approaches are necessary to ensure their validity rigorously. This study investigates the properties of solutions corresponding to congestion with sparse and dense waves. Specifically, we demonstrate the existence of traveling back/front, traveling pulse, and periodic traveling wave solutions in macroscopic models. All theorems are proven using phase-plane analysis without local bifurcation theory. The key to the proofs is the monotonicity of solution trajectories concerning implicit parameters that naturally appear in the models. We also examine the global bifurcation structure for heteroclinic, homoclinic, and periodic orbits, which correspond to traveling back/front, traveling pulse, and periodic traveling wave solutions, via the numerical continuation package HomCont/AUTO.
{"title":"Existence of traveling wave solutions in continuous optimal velocity models","authors":"Kota Ikeda , Toru Kan , Toshiyuki Ogawa","doi":"10.1016/j.physd.2024.134430","DOIUrl":"10.1016/j.physd.2024.134430","url":null,"abstract":"<div><div>In traffic flow theory, hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level car-following models. Self-organized wave propagation, which characterizes congestion, has been replicated in these macroscopic models. However, the existence of wave propagation has only been validated using numerical technique or formal analyses and has not yet been rigorously proven. Therefore, analytical approaches are necessary to ensure their validity rigorously. This study investigates the properties of solutions corresponding to congestion with sparse and dense waves. Specifically, we demonstrate the existence of traveling back/front, traveling pulse, and periodic traveling wave solutions in macroscopic models. All theorems are proven using phase-plane analysis without local bifurcation theory. The key to the proofs is the monotonicity of solution trajectories concerning implicit parameters that naturally appear in the models. We also examine the global bifurcation structure for heteroclinic, homoclinic, and periodic orbits, which correspond to traveling back/front, traveling pulse, and periodic traveling wave solutions, via the numerical continuation package HomCont/AUTO.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134430"},"PeriodicalIF":2.7,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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