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- Title
Bifurcation Behavior Analysis in a Predator-Prey Model.
- Authors
Wang, Nan; Zhao, Min; Yu, Hengguo; Dai, Chuanjun; Wang, Beibei; Wang, Pengfei
- Abstract
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.
- Subjects
PREDATION; BIFURCATION theory; ECOSYSTEMS; MATHEMATICAL models; STABILITY theory; COMPUTER simulation
- Publication
Discrete Dynamics in Nature & Society, 2016, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2016/3565316