Ratio-dependent predator–prey model: effect of environmental fluctuation and stability

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Published 1 February 2005 • 2005 IOP Publishing Ltd and London Mathematical Society
, , Citation M Bandyopadhyay and J Chattopadhyay 2005 Nonlinearity 18 913 DOI 10.1088/0951-7715/18/2/022

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Author affiliations

1 Department of Mathematics, Scottish Church College, Kolkata 700006, India

2 Embryology Research Unit, Indian Statistical Institute, Kolkata 700108, India

3 Author to whom any correspondence should be addressed.

Dates

  1. Received 27 April 2004
  2. Published

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0951-7715/18/2/913

Abstract

This paper deals with the problem of a ratio-dependent predator–prey model. The deterministic and stochastic behaviour of the model system around biologically feasible equilibria are studied. Conditions for which the deterministic model enter into Hopf-bifurcation are worked out. Stochastic stability of the system around positive interior equilibrium is studied. To substantiate our analytical findings numerical simulations are carried out for a hypothetical set of parameter values.

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10.1088/0951-7715/18/2/022