Dynamic behavior analysis of a feedback control predator-prey model with exponential fear effect and Hassell-Varley functional response. (English) Zbl 1508.92214
Summary: Considering that predator-induced fear effects affect the reproductive ability of the prey, as well as predator-predator interference during predation, a predator-prey model with exponential fear effect and Hassell-Varley functional response is proposed. The effects of fear level and the Hassell-Varley constant on the dynamics of the system are analyzed, and the results show that for predators that form tight groups, appropriately increasing the fear level can stabilize the system, while for other predators that do not form tight groups, the effect of fear on equilibrium stability is not particularly obvious. Besides, in order to reduce the negative impact of prey population on the environment, a feedback control strategy is applied to the system, and the existence and stability of order-\(n\) periodic solution are investigated by using the method of successive function, Poincaré map and Analogue to Poincaré criterion respectively. The periodic solution not only provides the conditions for control measures to be implemented, but also ensures that the prey population after control does not exceed a given level. To verify the correctness of the theoretical results obtained in this paper, numerical simulations for both models are carried out in MATLAB programs.
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