Extinction in Two-Species Nonlinear Discrete Competitive System
We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with a...
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| Main Authors: | , , , |
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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/10.1155/2016/2806405 |
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| _version_ | 1832551925559590912 |
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| author | Liqiong Pu Xiangdong Xie Fengde Chen Zhanshuai Miao |
| author_facet | Liqiong Pu Xiangdong Xie Fengde Chen Zhanshuai Miao |
| author_sort | Liqiong Pu |
| collection | DOAJ |
| description | We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results. |
| format | Article |
| id | doaj-art-09e8b29a7111408cb110de9076cd34ba |
| 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-09e8b29a7111408cb110de9076cd34ba2025-02-03T06:00:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/28064052806405Extinction in Two-Species Nonlinear Discrete Competitive SystemLiqiong Pu0Xiangdong Xie1Fengde Chen2Zhanshuai Miao3College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350108, ChinaDepartment of Mathematics, Ningde Normal University, Ningde, Fujian 352300, ChinaDepartment of Mathematics, Ningde Normal University, Ningde, Fujian 352300, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350108, ChinaWe propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.http://dx.doi.org/10.1155/2016/2806405 |
| spellingShingle | Liqiong Pu Xiangdong Xie Fengde Chen Zhanshuai Miao Extinction in Two-Species Nonlinear Discrete Competitive System Discrete Dynamics in Nature and Society |
| title | Extinction in Two-Species Nonlinear Discrete Competitive System |
| title_full | Extinction in Two-Species Nonlinear Discrete Competitive System |
| title_fullStr | Extinction in Two-Species Nonlinear Discrete Competitive System |
| title_full_unstemmed | Extinction in Two-Species Nonlinear Discrete Competitive System |
| title_short | Extinction in Two-Species Nonlinear Discrete Competitive System |
| title_sort | extinction in two species nonlinear discrete competitive system |
| url | http://dx.doi.org/10.1155/2016/2806405 |
| work_keys_str_mv | AT liqiongpu extinctionintwospeciesnonlineardiscretecompetitivesystem AT xiangdongxie extinctionintwospeciesnonlineardiscretecompetitivesystem AT fengdechen extinctionintwospeciesnonlineardiscretecompetitivesystem AT zhanshuaimiao extinctionintwospeciesnonlineardiscretecompetitivesystem |