Stability and Bifurcation Analysis in a Stage-Structured Predator-Prey Model with Delay

Abstract:

Hopf bifurcation occurs in most of dynamics systems when the influence from the past state varies. In modeling population dynamics, it is more reasonable taking into account the time delays. In this paper, a stage-structured predator-prey system with delay is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out.

• Periodical: Applied Mechanics and Materials (Volumes 513-517)
• Pages: 3723-3727
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.513-517.3723
• Online since: February 2014
• Authors: Hong Yan Wang*, Hong Mei Wang
• Keywords: Hopf Bifurcation, Predator-Prey, Stability

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