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Discrete Dynamics in Nature and Society - Volume 2016 2016, Article ID 3565316, 11 pages -

Research Article

School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China

School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Received 24 October 2015; Accepted 4 January 2016

Academic Editor: Taher S. Hassan

Copyright © 2016 Nan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.





Autor: Nan Wang, Min Zhao, Hengguo Yu, Chuanjun Dai, Beibei Wang, and Pengfei Wang

Fuente: https://www.hindawi.com/



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