TY - JOUR
T1 - Homoclinic Orbits of a Quadratic Isochronous System by the Perturbation-Incremental Method
AU - Li , Junhua
AU - Wang , Hailing
AU - Li , Zuxiong
AU - Chu , Zhusong
AU - Zhang , Chen
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 115
EP - 130
PY - 2021
DA - 2021/04
SN - 3
DO - http://doi.org/10.12150/jnma.2021.115
UR - https://global-sci.org/intro/article_detail/jnma/18781.html
KW - Perturbation-incremental method, Homoclinic orbits, Quadratic
isochronous system.
AB - <p style="text-align: justify;">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.</p>