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Zbl 1222.34099
Liu, Xia; Han, Maoan
Chaos and Hopf bifurcation analysis for a two species predator-prey system with prey refuge and diffusion. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 2, 1047-1061 (2011). ISSN 1468-1218

The authors consider a delayed predator-prey model with Holling type II functional response incorporating a constant prey refuge and diffusion. By analyzing the characteristic equation of the linearized system corresponding to the model, the authors study the local asymptotic stability of the positive equilibrium of the system. By choosing the time delay due to gestation as a bifurcation parameter, the existence of Hopf bifurcations at the positive equilibrium is established. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, using a numerical method, the influence of impulsive perturbations on the dynamics of the system is also investigated.
[Xinyu Song (Xinyang)]

MSC 2000:: *34K60 Applications of functional-differential equations
34K18 Bifurcation theory of functional differential equations
34K23 Complex (chaotic) behavior of solutions of FDE
92D25 Population dynamics
34K20 Stability theory of functional-differential equations
34K17 Transformation of functional-differential equations and systems
34K19 Invariant manifolds
34K45 Equations with impulses

Keywords: predator-prey model; diffusion; stability; Hopf bifurcation; center manifold theory

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