Existence of Center for Planar Differential Systems with Impulsive Perturbations
We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/479480 |
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| _version_ | 1849404823129030656 |
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| author | Dengguo Xu |
| author_facet | Dengguo Xu |
| author_sort | Dengguo Xu |
| collection | DOAJ |
| description | We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results. |
| format | Article |
| id | doaj-art-9a7ea1503dc342e986504d183c58b4e0 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9a7ea1503dc342e986504d183c58b4e02025-08-20T03:36:52ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/479480479480Existence of Center for Planar Differential Systems with Impulsive PerturbationsDengguo Xu0Department of Mathematics, Chuxiong Normal University, Chuxiong, Yunnan 675000, ChinaWe present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.http://dx.doi.org/10.1155/2015/479480 |
| spellingShingle | Dengguo Xu Existence of Center for Planar Differential Systems with Impulsive Perturbations Advances in Mathematical Physics |
| title | Existence of Center for Planar Differential Systems with Impulsive Perturbations |
| title_full | Existence of Center for Planar Differential Systems with Impulsive Perturbations |
| title_fullStr | Existence of Center for Planar Differential Systems with Impulsive Perturbations |
| title_full_unstemmed | Existence of Center for Planar Differential Systems with Impulsive Perturbations |
| title_short | Existence of Center for Planar Differential Systems with Impulsive Perturbations |
| title_sort | existence of center for planar differential systems with impulsive perturbations |
| url | http://dx.doi.org/10.1155/2015/479480 |
| work_keys_str_mv | AT dengguoxu existenceofcenterforplanardifferentialsystemswithimpulsiveperturbations |