Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 408, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.physd.2020.132479
Keywords
Poincare maps; Data-driven discovery; Multiscale system; Floquet theory
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Funding
- NSERC Postdoctoral Fellowship
- Air Force Office of Scientific Research (AFOSR) [FA9550-17-1-0329]
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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
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