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Stability and Hopf bifurcation in a prey-predator system with disease in the prey and two delays. (English) Zbl 1474.34482

Summary: This paper is concerned with a prey-predator system with disease in the prey and two delays. Local stability of the positive equilibrium of the system and existence of local Hopf bifurcation are investigated by choosing different combinations of the two delays as bifurcation parameters. For further investigation, the direction and the stability of the Hopf bifurcation are determined by using the normal form method and center manifold theorem. Finally, some numerical simulations are given to support the theoretical analysis.

MSC:

34K18 Bifurcation theory of functional-differential equations
92D25 Population dynamics (general)
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
37N25 Dynamical systems in biology
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