Leslie's prey-predator model in discrete time

We consider the Leslie's prey-predator model with discrete-time. This model is given by a non-linear evolution operator depending on five parameters. We show that this operator has two fixed points and define type of each fixed point depending on the parameters. Finding two invariant sets of the evolution operator we study the dynamical systems generated by the operator on each invariant set. Depending on the parameters we classify the dynamics between a predator and a prey of the Leslie's model.

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