ABSTRACT
As is well-known, heteroclinic and homoclinic orbits play an important role in the qualitative theory of dynamical systems. Dynamical systems with such orbits often exhibit a complicated global behavior, such as chaotic motions. So the study of such bifurcation has attracted much attention over the last ten years. From the theoretical point of view, it is much more difficult to study the bifurcations of heteroclinic or homoclinic orbits than that of equilibria, since the latter only concerns with the local behavior near a point, but the former requires global information and a more geometric approach. One of the analytical methods to deal with these global bifurcations is the so-called Melnikov method. This method is based on measuring the separation of the stable and unstable manifolds of the system and has been extensively studied, see, e. g. [1 — 13] and references therein.
