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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.

34K60Qualitative investigation and simulation of models
34K18Bifurcation theory of functional differential equations
34K19Invariant manifolds (functional-differential equations)
92D25Population dynamics (general)
Full Text: DOI
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