A Computer Comfirmation of Melnikov's Method Applied to Duffing-Van der Pol Equation

摘要

We check the validity of Melnikov's method for various orders of magnitude of a small parameter.As an example we investigate Duffing-Van der Pol's equation and its modified equation.We calculate errors between the result of Melnikov's method and that of computer simulation.As ε.result,it is found that for a larger ratio of the characteristic multipliers errors are more sensitive to the magnitude of ε.Further,we show that Melnikov's method can be applied to the autonomous case to obtain the condition under which the stable and unstable separatrices of the saddle equilibirum points interchange.