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Dynamics of a discrete ratio-dependent predator-prey system incorporating harvesting. (English) Zbl 1344.92128

Summary: In this paper, we consider a discrete ratio-dependent predator-prey system with harvesting effect. In order to investigate dynamical behaviors of this system, first we find out all fixed points of the system and then classify their stabilities by using their Jacobian matrices and local stability method. Next, we display some numerical examples to substantiate theoretical results and finally, we show numerically, by means of a bifurcation diagram, that various dynamical behaviors including cycles, periodic doubling bifurcation and chaotic bands can be existed.

MSC:

92D25 Population dynamics (general)
39A30 Stability theory for difference equations
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