The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits
Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed. Firstly, we verify the existence of heteroclinic orbits connecting two equilibrium points about the associ...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/6405853 |
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| author | Han Xu Yinlai Jin |
| author_facet | Han Xu Yinlai Jin |
| author_sort | Han Xu |
| collection | DOAJ |
| description | Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed. Firstly, we verify the existence of heteroclinic orbits connecting two equilibrium points about the associated systems for contrast structures in the corresponding phase space. Secondly, the asymptotic solutions of the contrast structures by the method of boundary layer functions and smooth connection are constructed. Finally, the uniform validity of the asymptotic expansion is defined and the existence of the smooth solutions is proved. |
| format | Article |
| id | doaj-art-fee6bd52ada9403389cb9aab3f69da3f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fee6bd52ada9403389cb9aab3f69da3f2025-02-03T01:07:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/64058536405853The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic OrbitsHan Xu0Yinlai Jin1School of Science, Linyi University, Linyi, Shandong 276005, ChinaSchool of Science, Linyi University, Linyi, Shandong 276005, ChinaSingularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed. Firstly, we verify the existence of heteroclinic orbits connecting two equilibrium points about the associated systems for contrast structures in the corresponding phase space. Secondly, the asymptotic solutions of the contrast structures by the method of boundary layer functions and smooth connection are constructed. Finally, the uniform validity of the asymptotic expansion is defined and the existence of the smooth solutions is proved.http://dx.doi.org/10.1155/2016/6405853 |
| spellingShingle | Han Xu Yinlai Jin The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits Discrete Dynamics in Nature and Society |
| title | The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits |
| title_full | The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits |
| title_fullStr | The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits |
| title_full_unstemmed | The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits |
| title_short | The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits |
| title_sort | contrast structures for a class of singularly perturbed systems with heteroclinic orbits |
| url | http://dx.doi.org/10.1155/2016/6405853 |
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