Bifurcation analysis of predator-prey systems with constant rate harvesting using non-standard discretization.
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.
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Mathematics & Physics Department, Qatar University, P. O. Box 2713, Doha, Qatar.