Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes
We study the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003) 1069–1075) First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by emp...
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Hindawi Limited
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/208167 |
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doaj-90de4fd65f2b4585be49fe864ae9e9f12020-11-25T01:09:22ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/208167208167Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II SchemesShengbin Yu0Sunshine College, Fuzhou University, Fuzhou, Fujian 350015, ChinaWe study the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003) 1069–1075) First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by employing the Fluctuation Lemma and Lyapunov direct method, respectively. The obtained results not only improve but also supplement existing ones.http://dx.doi.org/10.1155/2012/208167 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shengbin Yu |
| spellingShingle |
Shengbin Yu Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes Discrete Dynamics in Nature and Society |
| author_facet |
Shengbin Yu |
| author_sort |
Shengbin Yu |
| title |
Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes |
| title_short |
Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes |
| title_full |
Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes |
| title_fullStr |
Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes |
| title_full_unstemmed |
Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes |
| title_sort |
global asymptotic stability of a predator-prey model with modified leslie-gower and holling-type ii schemes |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2012-01-01 |
| description |
We study the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003) 1069–1075) First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by employing the Fluctuation Lemma and Lyapunov direct method, respectively. The obtained results not only improve but also supplement existing ones. |
| url |
http://dx.doi.org/10.1155/2012/208167 |
| work_keys_str_mv |
AT shengbinyu globalasymptoticstabilityofapredatorpreymodelwithmodifiedlesliegowerandhollingtypeiischemes |
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