Abstract
A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in (Formula presented.) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle.
Original language | English (US) |
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Journal | Journal of Dynamics and Differential Equations |
DOIs | |
State | Accepted/In press - Mar 5 2015 |
Keywords
- Approximate orbits
- Chaos
- Connecting orbits
- Heteroclinic cycle
- Homoclinic orbits
ASJC Scopus subject areas
- Analysis