Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function
A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient con...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/136707 |
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| _version_ | 1832555983950315520 |
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| author | Chongwu Zheng Fengqin Zhang Jianquan Li |
| author_facet | Chongwu Zheng Fengqin Zhang Jianquan Li |
| author_sort | Chongwu Zheng |
| collection | DOAJ |
| description | A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters. |
| format | Article |
| id | doaj-art-3dc69bda5f87481d8e9cfb2e98af850a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3dc69bda5f87481d8e9cfb2e98af850a2025-02-03T05:46:35ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/136707136707Stability Analysis of a Population Model with Maturation Delay and Ricker Birth FunctionChongwu Zheng0Fengqin Zhang1Jianquan Li2Department of Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, ChinaDepartment of Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, ChinaScience College, Air Force Engineering University, Xi'an 710051, ChinaA single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters.http://dx.doi.org/10.1155/2014/136707 |
| spellingShingle | Chongwu Zheng Fengqin Zhang Jianquan Li Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function Abstract and Applied Analysis |
| title | Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function |
| title_full | Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function |
| title_fullStr | Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function |
| title_full_unstemmed | Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function |
| title_short | Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function |
| title_sort | stability analysis of a population model with maturation delay and ricker birth function |
| url | http://dx.doi.org/10.1155/2014/136707 |
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