Switching effect of predation on prey species living in different habitats with arbitrary predatory rates II

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 habita...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2002-09, Vol.71 (9), p.2304-2309
Main Authors: BHATT, Balswaroop, OWEN, David, JAJU, Rameshwar P
Format: Article
Language:English
Subjects:
Applications
Biology, psychology, social sciences
Exact sciences and technology
Mathematics
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary: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.
ISSN:0031-9015
1347-4073
DOI:10.1143/jpsj.71.2304