Numerical continuation of homo/heteroclinic orbits with an oscillatory approach to stationary point

We formulate a boundary value problem to locate homoclinic or heteroclinic orbits approaching a stationary paint in an oscillatory manner so that velocity vectors on the orbit close to the stationary point are used rather than eigenvectors. A Newton method combined with multiple shooting can be used to numerically find the orbit truncated to a finite time interval. This is an extension of an earlier method proposed for 'nonoscillatory' homo/heteroclinics [1, 2]. We have incorporated this procedure into a continuation algorithm, so that a parameter dependence can be obtained. The method has been applied to Rossler system and can be applied to travelling waves.