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Homoclinic Orbits of a Quadratic IsochronousSystem by the Perturbation-incremental Method
  
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KeyWord:Perturbation-incremental method; Homoclinic orbits; Quadratic isochronous system
Author NameAffiliation
Junhua Li School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China 
Hailing Wang College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, China 
Zuxiong Li College of Mathematics and Statistics, China Three Gorges University, Chongqing 404199, China 
Zhusong Chu School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China 
Zhang Chen School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China 
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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. Assume 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.