On the Effect of Switching, Predation and Harvesting on Systems Consisting of One Predator and Two Prey Species Which Live in Different Habitats

B.S. Bhatt, D.R. Owen, R.P. Jaju

Abstract


The present work deals with two prey species living in two habitats and a predator specie which attacks the most abundant prey specie. The harvesting of both prey species is taken into account in the analysis. Non-zero equilibrium states have been examined with regard to their stability and the conditions for stability have been obtained. Using as a bifurcation parameter the conversion rate of prey to predator, conditions for a bifurcation to occur are obtained. A Hopf bifurcation theorem has been derived. In the investigations we used six forms of predation and harvesting rates to analyze the theory, however, we display graphical results for
only one particular case.

Full Text: PDF DOI: 10.5539/jmr.v3n3p12

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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