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Chaotic dynamics of a discrete prey-predator model with Holling type II. (English) Zbl 1154.37335

Summary: A discrete-time prey-predator model with Holling type II is investigated. For this model, the existence and stability of three fixed points are analyzed. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for different parameters of the model. The fractal dimension of a strange attractor of the model was also calculated. Numerical simulations show that the discrete model exhibits rich dynamics compared with the continuous model, which means that the present model is a chaotic, and complex one.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
37N25 Dynamical systems in biology
92D25 Population dynamics (general)
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