Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed DelayReportar como inadecuado




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Abstract and Applied Analysis - Volume 2014 2014, Article ID 184174, 15 pages -

Research Article

Institute of Systems Science, Northeastern University, Shenyang 110004, China

State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang 110004, China

Received 3 February 2014; Accepted 28 March 2014; Published 27 April 2014

Academic Editor: Qun Lin

Copyright © 2014 Chao Liu and Qingling Zhang. 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

We propose a prey predator model with stage structure for prey. A discrete delay and a distributed delay for predator described by an integral with a strong delay kernel are also considered. Existence of two feasible boundary equilibria and a unique interior equilibrium are analytically investigated. By analyzing associated characteristic equation, local stability analysis of boundary equilibrium and interior equilibrium is discussed, respectively. It reveals that interior equilibrium is locally stable when discrete delay is less than a critical value. According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied based on normal form theory and center manifold theorem. Numerical simulations are carried out to show consistency with theoretical analysis.





Autor: Chao Liu and Qingling Zhang

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



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