Periodic Solutions of a Time Delay Stage-structured Prey-predator Model
Yanqiu Li *
Department of Applied Mathematics, Nanjing University of Technology, Nanjing 211816, China
Wei Duan Duan
Petro-China West-East Gas Pipeline Company, Yangzhou 225009, China.
Shujian Ma
Department of Applied Mathematics, Nanjing University of Technology, Nanjing 211816, China.
*Author to whom correspondence should be addressed.
Abstract
The dynamics of a time delay stage-structured prey-predator model is investigated. Firstly, through the analysis of the eigenvalues, the effect of time delay on the stability of the positive equilibrium and the existence of Hopf bifurcation are obtained. Further, the stability and the direction of Hopf bifurcation periodic solution near the first critical value are given utilizing the normal form method and the center manifold theorem.
Keywords: Stability, time delay, Hopf bifurcation, stage structure.