科研之友
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摘要
In this paper, we formulate a two-dimensional autonomous predator-prey model with state-dependent impulsive effects and square root response function. The square root response function indicates that the prey population gather together for self-defense purposes. Firstly, we prove that the system has semitrivial periodic solution under some conditions. Furthermore, by the Poincare map and the theory of impulsive differential equations, the existence and stability of positive order-1 or order-2 periodic solution of the system are investigated in detail. The validity of all results is illustrated by numerical simulations.
