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Hopf bifurcation analysis of a predator-prey system with Holling type IV functional response and time delay. (English) Zbl 1187.34116

This paper is concerned with a predator-prey system with Holling type IV functional response and time delay. By choosing the delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are analyzed. Based on the normal form and the center manifold theory, the formulas for determining the properties of Hopf bifurcation of the predator-prey system are derived. Finally, to support these theoretical results, some numerical simulations are given to illustrate the results.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K19 Invariant manifolds of functional-differential equations
92D25 Population dynamics (general)
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