Bifurcation Behavior Analysis in a Predator-Prey Model
A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and s...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/3565316 |
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| _version_ | 1832555516087238656 |
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| author | Nan Wang Min Zhao Hengguo Yu Chuanjun Dai Beibei Wang Pengfei Wang |
| author_facet | Nan Wang Min Zhao Hengguo Yu Chuanjun Dai Beibei Wang Pengfei Wang |
| author_sort | Nan Wang |
| collection | DOAJ |
| description | A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation), which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems. |
| format | Article |
| id | doaj-art-2169d1c2475e435bbcc4a923bb6bf965 |
| 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-2169d1c2475e435bbcc4a923bb6bf9652025-02-03T05:48:01ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/35653163565316Bifurcation Behavior Analysis in a Predator-Prey ModelNan Wang0Min Zhao1Hengguo Yu2Chuanjun Dai3Beibei Wang4Pengfei Wang5School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaA predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation), which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.http://dx.doi.org/10.1155/2016/3565316 |
| spellingShingle | Nan Wang Min Zhao Hengguo Yu Chuanjun Dai Beibei Wang Pengfei Wang Bifurcation Behavior Analysis in a Predator-Prey Model Discrete Dynamics in Nature and Society |
| title | Bifurcation Behavior Analysis in a Predator-Prey Model |
| title_full | Bifurcation Behavior Analysis in a Predator-Prey Model |
| title_fullStr | Bifurcation Behavior Analysis in a Predator-Prey Model |
| title_full_unstemmed | Bifurcation Behavior Analysis in a Predator-Prey Model |
| title_short | Bifurcation Behavior Analysis in a Predator-Prey Model |
| title_sort | bifurcation behavior analysis in a predator prey model |
| url | http://dx.doi.org/10.1155/2016/3565316 |
| work_keys_str_mv | AT nanwang bifurcationbehavioranalysisinapredatorpreymodel AT minzhao bifurcationbehavioranalysisinapredatorpreymodel AT hengguoyu bifurcationbehavioranalysisinapredatorpreymodel AT chuanjundai bifurcationbehavioranalysisinapredatorpreymodel AT beibeiwang bifurcationbehavioranalysisinapredatorpreymodel AT pengfeiwang bifurcationbehavioranalysisinapredatorpreymodel |