Hopf bifurcation analysis for a semiratio-dependent predator-prey system with two delays. (English) Zbl 1297.34094
Summary: This paper is concerned with a semiratio-dependent predator-prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 34K18 | Bifurcation theory of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K17 | Transformation and reduction of functional-differential equations and systems, normal forms |
| 34K19 | Invariant manifolds of functional-differential equations |
| 92D25 | Population dynamics (general) |
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