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Dynamic analysis of an impulsively controlled predator-prey model with Holling type IV functional response. (English) Zbl 1233.92079
Summary: The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system are also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics.

MSC:
92D40 Ecology
34A37 Ordinary differential equations with impulses
34H05 Control problems involving ordinary differential equations
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