Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system ha...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/8075381 |
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| _version_ | 1832545381759582208 |
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| author | Yuzhen Mi |
| author_facet | Yuzhen Mi |
| author_sort | Yuzhen Mi |
| collection | DOAJ |
| description | This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution. |
| format | Article |
| id | doaj-art-8c7cb77fc71241ee95b3f62bd3787cbc |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8c7cb77fc71241ee95b3f62bd3787cbc2025-02-03T07:25:57ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/80753818075381Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small PerturbationYuzhen Mi0Department of Mathematics, Lingnan Normal University, Zhanjiang, Guangdong 524048, ChinaThis paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.http://dx.doi.org/10.1155/2016/8075381 |
| spellingShingle | Yuzhen Mi Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation Journal of Function Spaces |
| title | Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation |
| title_full | Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation |
| title_fullStr | Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation |
| title_full_unstemmed | Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation |
| title_short | Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation |
| title_sort | existence of generalized homoclinic solutions of lotka volterra system under a small perturbation |
| url | http://dx.doi.org/10.1155/2016/8075381 |
| work_keys_str_mv | AT yuzhenmi existenceofgeneralizedhomoclinicsolutionsoflotkavolterrasystemunderasmallperturbation |