Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 11, Iss. 3, July, 2007, pp. 333-348
@2007 Society for Chaos Theory in Psychology & Life Sciences


Bifurcation Analysis of Predator-Prey Systems with Constant Rate Harvesting Using Non-Standard Discretization

G. H. Erjaee, Shiraz University, Shiraz, Iran

Abstract: We formulate and apply non-standard discretization methods that enable us to study the saddle, elliptic and parabolic cases of the predator-prey system with constant rate harvesting as difference dynamical systems. Our models have the same qualitative features as their corresponding continuous models. By choosing appropriate bifurcation parameters, we combine analytical and numerical investigations to produce interesting global bifurcation diagrams, including saddle-node, Hopf and Bogdanov-Takens bifurcations.

Keywords: dynamical systems, difference equations, nonstandard schemes