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Using Melnikov's method to solve Silnikov's problems*

Published online by Cambridge University Press:  14 November 2011

Xiao-Biao Lin
Xiao-Biao Lin
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, U.S.A.
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Synopsis

A function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's main theorems and a retreatment of a singularly perturbed delay differential equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 3-4 , 1990 , pp. 295 - 325
Copyright
Copyright © Royal Society of Edinburgh 1990

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