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 velo city vectors on the orbit close to the stationary point are used rather tha n 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/heter oclinics [1, 2]. We have incorporated this procedure into a continuation al gorithm, so that a parameter dependence can be obtained. The method has bee n applied to Rossler system and can be applied to travelling waves.