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Existence and stability of periodic solution of a predator-prey model with state-dependent impulsive effects. (English) Zbl 1185.34123

The authors investigate the dynamic behavior of a class of predator-prey systems with state-dependent impulsive effects by releasing natural enemies and spraying pesticides at different thresholds. By using the Poincaré map and the properties of the Lambert function, the authors obtain some sufficient conditions for the existence and stability of semi-trivial solutions and positive periodic solutions. Numerical results are also carried out to illustrate the main results.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K45 Functional-differential equations with impulses
34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
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