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Dynamical analysis in a delayed predator-prey model with two delays. (English) Zbl 1250.34068

Summary: A class of Beddington-DeAngelis functional response predator-prey model is considered. Conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcating periodic solution are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K19 Invariant manifolds of functional-differential equations
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References:

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