Poincare maps for multiscale physics discovery and nonlinear Floquet theory

PHYSICA D-NONLINEAR PHENOMENA

卷:408

Article

Bramburger, Jason J.^1,2  Kutz, J. Nathan³ 

[1] Brown Univ, Div Appl Math, Providence, RI 02906 USA

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8P 5C2, Canada

[3] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

关键词: Poincare maps;    Data-driven discovery;    Multiscale system;    Floquet theory;   

DOI  :  10.1016/j.physd.2020.132479

来源: Elsevier

【 摘 要 】

Poincare maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this manuscript we propose a method of data-driven discovery of Poincare maps based upon sparse regression techniques, specifically the sparse identification of nonlinear dynamics (SINDy) algorithm. This work can be used to determine the dynamics on and near invariant manifolds of a given dynamical system, as well as provide long-time forecasting of the coarse-grained dynamics of multiscale systems. Moreover, the method provides a mathematical formalism for determining nonlinear Floquet theory for the stability of nonlinear periodic orbits. The methods are applied to a range of examples including both ordinary and partial differential equations that exhibit periodic, quasi-periodic, and chaotic behavior. (C) 2020 Elsevier B.V. All rights

【 授权许可】

Free