HOMOCLINIC ORBITS OF THE TRUNCATED SYSTEMS OF SINE-GORDON EQUATION 1)

In this paper the existence of the homoclinic orbits defined by Wiggins is proved, by use of ODE on the generalized asymptotic inertial manifold for the Sine Gordon equation. We give explicit conditions (in terms of the system parameters) for the model to possess a symmetric pair of homoclinic orbits to a fixed of saddle focus type, chaotic dynamics follow from a theorem of Silnikov. This provides a mechnism for chaotic dynamics geometrically similar to that observed by Bishop et al.,namely, a random...