Dynamical Analysis in a Delayed Predator-Prey System with Stage-Structure for Both the Predator and the Prey. (19th February 2014)

• Record Type: Journal Article
• Authors: Zhang, Zizhen; Yang, Huizhong
• Other Names: Zhang Zhengqiu Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-02-19
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/909238
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : A predator-prey system with two delays and stage-structure for both the predator and the prey is considered. Sufficient conditions for the local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation. Specially, the direction of the Hopf bifurcation and the stability of the periodic solutions bifurcating from the Hopf bifurcation are determined by applying the normal form theory and center manifold argument. Some numerical simulations for justifying the theoretical analysis are also provided.