Homoclinic Flip Bifurcations in Conservative Reversible Systems

Abstract

In this paper, flip bifurcations of homoclinic orbits in conservative reversible systems are analyzed. In such systems, orbit-flip and inclination-flip bifurcations occur simultaneously. It is shown that multi-pulses either do not bifurcate at all at flip bifurcation points or else bifurcate simultaneously to both sides of the bifurcation point. An application to a fifth-order model of water waves is given to illustrate the results, and open problems regarding the PDE stability of multi-pulses are outlined. © Springer Basel 2013.