Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ANALYSIS OF A NONAUTONOMOUS PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE AND TIME DELAY

  • Samanta, G.P. (Department of Mathematics, Bengal Engineering and Science University) ;
  • Garain, D.N. (Department of Mathematics, S.K.M. University)
  • Received : 2010.03.05
  • Accepted : 2010.07.28
  • Published : 2011.05.30
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Abstract

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

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References

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