A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions

Koki Nitta, Nobito Yamamoto, Kaname Matsue

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a verification method for specification of homoclinic orbits as application of our previous work for constructing local Lyapunov functions by verified numerics. Our goal is to specify parameters appeared in the given systems of ordinary differential equations (ODEs) which admit homoclinic orbits to equilibria. Here we restrict ourselves to cases that each equilibrium is independent of parameters. The feature of our methods consists of Lyapunov functions, integration of ODEs by verified numerics, and Brouwer’s coincidence theorem on continuous mappings. Several techniques for constructing continuous mappings from a domain of parameter vectors to a region of the phase space are shown. We present numerical examples for problems in 3 and 4-dimensional cases.

Original languageEnglish
JournalJapan Journal of Industrial and Applied Mathematics
DOIs
Publication statusAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

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