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Stability and bifurcation analysis on a ratio-dependent predator-prey model with prey dispersal and time delay. (English) Zbl 1186.34123
Summary: A ratio-dependent predator-prey model with prey dispersal and time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium and the existence of Hopf bifurcations are established. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of bifurcating periodic solutions. By means of an iteration technique, sufficient conditions are obtained to guarantee the positive equilibrium to be globally attractive. Numerical simulations are carried out to illustrate the main results.
MSC:
34K60Qualitative investigation and simulation of models
92D25Population dynamics (general)
34K20Stability theory of functional-differential equations
34K18Bifurcation theory of functional differential equations
34K13Periodic solutions of functional differential equations
34K19Invariant manifolds (functional-differential equations)
34K17Transformation and reduction of functional-differential equations and systems; normal forms