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

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  • Timsina, Archana Neupane
  • Mireles James, J.D.

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.

Suggested Citation

  • Timsina, Archana Neupane & Mireles James, J.D., 2022. "Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005550
    DOI: 10.1016/j.chaos.2022.112345
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    References listed on IDEAS

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    1. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
    2. Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
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