Homoclinic Orbits of a Quadratic Isochronous System by the Perturbation-Incremental Method

Abstract

In this paper, the perturbation-incremental method is presented for the analysis of a quadratic isochronous system. This method combines the remarkable characteristics of the perturbation method and the incremental method. The first step is the perturbation method. Assuming that the parameter $\lambda$ is small, i.e. $\lambda\approx0$, the initial expression of the homoclinic orbit is obtained. The second step is the parameter incremental method. By extending the solution corresponding to small parameters to large parameters, we can get the analytical-expressions of homoclinic orbits.