The Bifurcations of Countable Connections from a Twisted Heteroclinic Loop
- 1 May 1991
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 22 (3) , 653-679
- https://doi.org/10.1137/0522041
Abstract
Codimension-two bifurcation phenomena associated with nondegenerate heteroclinic loops are studied. The bifurcation curves of homoclinic orbits in the parameter space are characterized by the twist structure of the heteroclinic loops at the bifurcation points. Among other things, it is shown that heteroclinic orbits with any given winding number around a doubly twisted heteroclinic loop must bifurcate. Applications of these bifurcation phenomena are also discussed.Keywords
This publication has 17 references indexed in Scilit:
- EXPONENTIAL EXPANSION WITH PRINCIPAL EIGENVALUESInternational Journal of Bifurcation and Chaos, 1996
- Homoclinic bifurcation at resonant eigenvaluesJournal of Dynamics and Differential Equations, 1990
- The Bifurcation of Homoclinic and Periodic Orbits from Two Heteroclinic OrbitsSIAM Journal on Mathematical Analysis, 1990
- The Sil'nikov problem, exponential expansion, strong λ-lemma, C1-linearization, and homoclinic bifurcationJournal of Differential Equations, 1989
- Homoclinic and heteroclinic bifurcations of Vector fieldsJapan Journal of Applied Mathematics, 1988
- Stability of the travelling wave solution of the FitzHugh-Nagumo systemTransactions of the American Mathematical Society, 1984
- Single and Multiple Pulse Waves for the FitzHugh–NagumoSIAM Journal on Applied Mathematics, 1982
- Double Impulse Solutions in Nerve Axon EquationsSIAM Journal on Applied Mathematics, 1982
- Differential TopologyPublished by Springer Nature ,1976
- Nerve Axon Equations: III Stability of the Nerve ImpulseIndiana University Mathematics Journal, 1972