Switching effect of predation on a small size prey species living in two different habitats

Balswaroop Bhatt, Qamar J A Khan, Ranieshwar P. Jaju

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Abstract

A Mathematical model with one prey species living in two different habitats and a predator where the predatory rate diminishes at low population density of prey is investigated. Two habitats are separated by a barrier and prey species is able to disperse among two different habitats at some cost of the population. The stability analysis is carried out for non-zero equilibrium values. Using rate of conversion of the prey to predator as bifurcation parameter, the necessary and sufficient condition for a Hopf bifurcation to occur are derived. It is shown numerically that predation rate does not always have stabilizing effect for the prey-predator system.

Original languageEnglish
Pages (from-to)3133-3137
Number of pages5
JournalJournal of the Physical Society of Japan
Volume69
Issue number9
Publication statusPublished - Sep 2000

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Keywords

  • Differential equations
  • Hopf bifurcation
  • Predator
  • Prey
  • Stability
  • Switching

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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