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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 Name | Affiliation | | 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. |
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