Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control

Yangyang Su and Tongqian Zhang
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Yangyang Su: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Tongqian Zhang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2022, vol. 10, issue 8, 1-23

Abstract: In this paper, a predator–prey model with fear effect and impulsive state control is proposed and analyzed. By constructing an appropriate Poincaré map, the dynamic properties of the system, including the existence, nonexistence, and stability of periodic solutions are studied. More specifically, based on the biological meaning, the pulse and the phase set are firstly defined in different regions as well as the corresponding Poincaré map. Subsequently, the properties of the Poincaré map are analyzed, and the existence of a periodic solution for the system is investigated according to the properties of the Poincaré map. We found that the existence of the periodic solution for the system completely depends on the property of the Poincaré map. Finally, several examples containing numerical simulations verify the obtained theoretical result.

Keywords: fear effect; impulsive state feedback control; Poincaré map; order-1 periodic solution; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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