Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems

Archana Neupane Timsina and J.D. Mireles James

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: We develop a multiple shooting parameterization method for studying stable/unstable manifolds attached to periodic orbits of systems whose dynamics is determined by an implicit rule. We represent the local invariant manifold using high order polynomials and show that the method leads to efficient numerical calculations. We implement the method for several example systems in dimension two and three. The resulting manifolds provide useful information about the orbit structure of the implicit system even in the case that the implicit relation is neither invertible nor single-valued.

Keywords: Implicitly defined dynamical systems; Computational methods; Invariant manifolds; Periodic orbits; Parameterization method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005550

DOI: 10.1016/j.chaos.2022.112345

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