Nonlinear Dynamics

, 58:497

Bifurcation and stability analysis in predator–prey model with a stage-structure for predator

Original Paper

DOI: 10.1007/s11071-009-9495-y

Cite this article as:
Sun, X., Huo, H. & Xiang, H. Nonlinear Dyn (2009) 58: 497. doi:10.1007/s11071-009-9495-y

Abstract

A predator–prey system with Holling type II functional response and stage-structure for predator is presented. The stability and Hopf bifurcation of this model are studied by analyzing the associated characteristic transcendental equation. Further, an explicit formula for determining the stability and the direction of periodic solutions bifurcating from positive equilibrium is derived by the normal form theory and center manifold argument. Some numerical simulations are also given to illustrate our results.

Keywords

Hopf bifurcationStabilityTime delayPredator–prey system

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Applied MathematicsLanzhou University of TechnologyLanzhouPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsTianshui Normal UniversityTianshuiPeople’s Republic of China