Abstract
We consider a family of partial functional differential equations which has a homoclinic orbit asymptotic to an isolated equilibrium point at a critical value of the parameter. Under some technical assumptions, we show that a unique stable periodic orbit bifurcates from the homoclinic orbit. Our approach follows the ideas of Šil'nikov for ordinary differential equations and of Chow and Deng for semilinear parabolic equations and retarded functional differential equations.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1293-1322 |
| Number of pages | 30 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 9 |
| Issue number | 5 |
| DOIs | |
| State | Published - Sep 2003 |
Keywords
- Bifurcation
- Homoclinic orbit
- Partial functional differential equations
- Periodic solutions
- Stable and unstable manifolds
- Variation of constant formula
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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Ruan, S., Wei, J., & Wu, J. (2003). Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete and Continuous Dynamical Systems, 9(5), 1293-1322. https://doi.org/10.3934/dcds.2003.9.1293