Journal of Nonlinear Science最新文献_第9页

Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds 未知不变曲面附近慢-快随机系统的非线性模型还原

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-08 DOI: 10.1007/s00332-023-09998-8

Felix X.-F. Ye, Sichen Yang, Mauro Maggioni

{"title":"Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds","authors":"Felix X.-F. Ye, Sichen Yang, Mauro Maggioni","doi":"10.1007/s00332-023-09998-8","DOIUrl":"https://doi.org/10.1007/s00332-023-09998-8","url":null,"abstract":"We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics and high-dimensional, large fast modes. Given only access to a black-box simulator from which short bursts of simulation can be obtained, we design an algorithm that outputs an estimate of the invariant manifold, a process of the effective stochastic dynamics on it, which has averaged out the fast modes, and a simulator thereof. This simulator is efficient in that it exploits of the low dimension of the invariant manifold, and takes time-steps of size dependent on the regularity of the effective process, and therefore typically much larger than that of the original simulator, which had to resolve the fast modes. The algorithm and the estimation can be performed on the fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"229 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138562677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Error Estimates of hp Spectral Element Methods in Nonlinear Optimal Control Problem 非线性最优控制问题中hp谱元方法的误差估计

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-12-01 DOI: 10.1007/s00332-023-09991-1

Xiuxiu Lin, Yanping Chen, Yunqing Huang

引用次数: 0

Well-Posedness and Stability Analysis of a Landscape Evolution Model 景观演化模型的拟合性与稳定性分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-11-24 DOI: 10.1007/s00332-023-09997-9

Julie Binard, Pierre Degond, Pascal Noble

引用次数: 0

Cognitive Consumer-Resource Spatiotemporal Dynamics with Nonlocal Perception 非局部感知的认知消费者-资源时空动态

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-11-18 DOI: 10.1007/s00332-023-09996-w

Yongli Song, Hao Wang, Jinfeng Wang

{"title":"Cognitive Consumer-Resource Spatiotemporal Dynamics with Nonlocal Perception","authors":"Yongli Song, Hao Wang, Jinfeng Wang","doi":"10.1007/s00332-023-09996-w","DOIUrl":"https://doi.org/10.1007/s00332-023-09996-w","url":null,"abstract":"Nonlocal perception is crucial to the mechanistic modeling of cognitive animal movement. We formulate a diffusive consumer-resource model with nonlocal perception on resource availability, where resource dynamics is explicitly modeled, to investigate the influence of nonlocal perception on stability and spatiotemporal patterns. For the finite domain, nonlocal perception described by two common types of resource detection function (spatial average or Green function) has no impact on the stability of the spatially homogeneous steady state. For the infinite domain, nonlocal perception described by the Laplacian or Gaussian detection function has no impact on stability either; however, the top-hat detection function can destabilize the spatially homogeneous steady state when the rate of perceptual movement is large and the detection scale belongs to an appropriate interval. Using the more realistic top-hat perception kernel, we investigate the influence of the detection scale, the perceptual movement rate and the resource’s carrying capacity on the spatiotemporal patterns and find the stripe spatial patterns, oscillatory patterns with different spatial profiles as well as spatiotemporal chaos.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"138 ","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Oscillations in a Fully Connected Network of Leaky Integrate-and-Fire Neurons with a Poisson Spiking Mechanism 具有泊松尖峰机制的漏积分-火神经元全连接网络的振荡

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-11-17 DOI: 10.1007/s00332-023-09995-x

Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu

引用次数: 0

Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems 三时间尺度系统中折叠极限环流形的几何爆破

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2023-11-16 DOI: 10.1007/s00332-023-09987-x

S. Jelbart, C. Kuehn, S.-V. Kuntz

{"title":"Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems","authors":"S. Jelbart, C. Kuehn, S.-V. Kuntz","doi":"10.1007/s00332-023-09987-x","DOIUrl":"https://doi.org/10.1007/s00332-023-09987-x","url":null,"abstract":"Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of ‘stationary’ multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast subsystem, particularly when combined with a method of desingularisation known as blow-up. The theory for ‘oscillatory’ multiple time-scale systems which possess a limit cycle manifold instead of (or in addition to) a critical manifold is less developed, particularly in the non-normally hyperbolic regime. We use the blow-up method to analyse the global oscillatory transition near a regular folded limit cycle manifold in a class of three time-scale ‘semi-oscillatory’ systems with two small parameters. The systems considered behave like oscillatory systems as the smallest perturbation parameter tends to zero, and stationary systems as both perturbation parameters tend to zero. The additional time-scale structure is crucial for the applicability of the blow-up method, which cannot be applied directly to the two time-scale oscillatory counterpart of the problem. Our methods allow us to describe the asymptotics and strong contractivity of all solutions which traverse a neighbourhood of the global singularity. Our main results cover a range of different cases with respect to the relative time-scale of the angular dynamics and the parameter drift. We demonstrate the applicability of our results for systems with periodic forcing in the slow equation, in particular for a class of Liénard equations. Finally, we consider a toy model used to study tipping phenomena in climate systems with periodic forcing in the fast equation, which violates the conditions of our main results, in order to demonstrate the applicability of classical (two time-scale) theory for problems of this kind.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"21 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis 带噪声的随机梯度下降机器学习第二部分:连续时间分析

2区数学

Journal of Nonlinear Science Pub Date : 2023-11-15 DOI: 10.1007/s00332-023-09992-0

Stephan Wojtowytsch

引用次数: 2

Phase-Locked Solutions of a Coupled Pair of Nonidentical Oscillators 非同振子耦合对的锁相解

2区数学

Journal of Nonlinear Science Pub Date : 2023-11-11 DOI: 10.1007/s00332-023-09989-9

Kuan-Wei Chen, Chih-Wen Shih

引用次数: 0

Phase-Amplitude Coordinate-Based Neural Networks for Inferring Oscillatory Dynamics 基于相位振幅坐标的振动动力学推理神经网络

2区数学

Journal of Nonlinear Science Pub Date : 2023-11-11 DOI: 10.1007/s00332-023-09994-y

Talha Ahmed, Dan Wilson

引用次数: 0

A Nonlocal Reaction-Diffusion Model of West Nile Virus with Vertical Transmission 西尼罗病毒垂直传播的非局部反应扩散模型

2区数学

Journal of Nonlinear Science Pub Date : 2023-11-07 DOI: 10.1007/s00332-023-09985-z

Feng-Bin Wang, Ruiwen Wu, Xiao-Qiang Zhao

引用次数: 0