Switching Effect of Predation on Prey Species Living in Different Habitats with Arbitrary Predatory Rates II.

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  • Bhatt Balswaroop
    Department of Mathematics and Computer Science, The University of the West Indies, St. Augustine, Trindad and Tobago
  • Owen David
    Department of Mathematics and Computer Science, The University of the West Indies, St. Augustine, Trindad and Tobago
  • Jaju Rameshwar P.
    Department of Computer Science, Faculty of Science, University of Swaziland, P. O. BOX 4, Kwaluseni Swaziland, Southern Africa

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  • Switching Effect of Predation on Prey Species Living in Different Habitats with Arbitrary Predatory Rates 2

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The present paper extends previous work by Bhatt et al. [J. Phys. Soc. Jpn. 69 (2000) 3133] referred as Part I. It deals with the switching effect of predation on prey species living in two habitats when the predatory rates are arbitrary. The predator feeds preferentially on the more abundant habitats population. Two habitats have been separated by a barrier so that the prey species is able to disperse among them at some cost of the population. The stability analysis has been carried out for non-zero equilibrium values. Using the conversion rate of the prey to predator as a bifurcation parameter, necessary and sufficient conditions for a Hopf bifurcation to occur have been derived. Two particular cases of predatory rates, namely, (i) multiplicative case and (ii) exponential case have been derived.

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