## The effect of dispersal on the permanence of a predator-prey system with time delay.(English)Zbl 1142.34055

Summary: A predator-prey model with prey dispersal and time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the nonnegative equilibria is discussed. By using an iteration technique, a threshold is derived for the permanence and extinction of the proposed model. Numerical simulations are carried out to illustrate the main results.

### MSC:

 34K60 Qualitative investigation and simulation of models involving functional-differential equations 92D25 Population dynamics (general) 34K25 Asymptotic theory of functional-differential equations 34K20 Stability theory of functional-differential equations
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### References:

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