Homoclinic Twist Bifurcation in a System of Two Coupled Oscillators

摘要

The qualitative analysis of the dynamics in the vicinity of a homoclinic twist211u001epoint in a two parameter family of Z(sub 2)-symmetric automonomous ordinary 211u001edifferential equations in four dimensions has been performed. A variant of the 211u001eLyapunov-Schmidt reduction method has been used to prove the existence of n times 211u001ewinding homoclinic loops, periodic orbits limiting on these homoclinic orbits and 211u001enon-periodic orbits. Theoretical results supplement numerical results on the 211u001ecomputation of nonsymmetric homoclinic orbits in a system of two Josephson 211u001ejunctions, in order to check the relevance of these computations.