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Complex dynamics of a Holling type II prey-predator system with state feedback control. (English) Zbl 1203.34071
Summary: The complex dynamics of a Holling type II prey-predator system with impulsive state feedback control is studied in both theoretical and numerical ways. Sufficient conditions for the existence and stability of positive periodic solutions are obtained by using the Poincaré map and the analogue of the Poincaré criterion. A qualitative analysis shows that the positive periodic solution bifurcates from a solution through a fold bifurcation. The bifurcation diagrams, Lyapunov exponents, and phase portraits are illustrated by an example, in which the chaotic solutions appear via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C28 Complex behavior and chaotic systems of ordinary differential equations
92D25 Population dynamics (general)
34A37 Ordinary differential equations with impulses
93B52 Feedback control
34C25 Periodic solutions to ordinary differential equations
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