Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation
This paper is concerned with a new predator-prey model with stage structure on prey, in which the immature prey and the mature prey are preyed on by predator. We think that the model is more realistic and interesting than the one in which only the immature prey or the mature prey is consumed by pred...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/512817 |
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| _version_ | 1850172261139480576 |
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| author | Liu Yang Shouming Zhong |
| author_facet | Liu Yang Shouming Zhong |
| author_sort | Liu Yang |
| collection | DOAJ |
| description | This paper is concerned with a new predator-prey model with stage structure on prey, in which the immature prey and the mature prey are preyed on by predator. We think that the model is more realistic and interesting than the one in which only the immature prey or the mature prey is consumed by predator. Our work shows that the stochastic model and its corresponding deterministic system have a unique global positive solution and the positive solution is global asymptotic stability for each model. If the positive equilibrium point of the deterministic system is globally stable, then the stochastic model will preserve the nice property provided that the noise
is sufficiently small. Results are analyzed with the help of graphical illustrations. |
| format | Article |
| id | doaj-art-cfc0c90d22df48a59da4ff1276c989f8 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-cfc0c90d22df48a59da4ff1276c989f82025-08-20T02:20:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/512817512817Global Stability of a Stage-Structured Predator-Prey Model with Stochastic PerturbationLiu Yang0Shouming Zhong1School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 611731, ChinaThis paper is concerned with a new predator-prey model with stage structure on prey, in which the immature prey and the mature prey are preyed on by predator. We think that the model is more realistic and interesting than the one in which only the immature prey or the mature prey is consumed by predator. Our work shows that the stochastic model and its corresponding deterministic system have a unique global positive solution and the positive solution is global asymptotic stability for each model. If the positive equilibrium point of the deterministic system is globally stable, then the stochastic model will preserve the nice property provided that the noise is sufficiently small. Results are analyzed with the help of graphical illustrations.http://dx.doi.org/10.1155/2014/512817 |
| spellingShingle | Liu Yang Shouming Zhong Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation Discrete Dynamics in Nature and Society |
| title | Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation |
| title_full | Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation |
| title_fullStr | Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation |
| title_full_unstemmed | Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation |
| title_short | Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation |
| title_sort | global stability of a stage structured predator prey model with stochastic perturbation |
| url | http://dx.doi.org/10.1155/2014/512817 |
| work_keys_str_mv | AT liuyang globalstabilityofastagestructuredpredatorpreymodelwithstochasticperturbation AT shoumingzhong globalstabilityofastagestructuredpredatorpreymodelwithstochasticperturbation |