Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance

Yuke Zhang and Xinzhu Meng ()
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Yuke Zhang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Xinzhu Meng: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2022, vol. 10, issue 16, 1-18

Abstract: This paper proposes a stochastic predator–prey model with hunting cooperation and nonlinear stochastic disturbance, and focuses on the effects of nonlinear white noise and hunting cooperation on the populations. First, we present the thresholds R 1 and R 2 for extinction and persistence in mean of the predator. When R 1 is less than 0, the predator population is extinct; when R 2 is greater than 0, the predator population is persistent in mean. Moreover, by establishing suitable Lyapunov functions, we investigate the threshold R 0 for the existence of a unique ergodic stationary distribution. At last, we carry out the numerical simulations. The results show that white noise is harmful to the populations and hunting cooperation is beneficial to the predator population.

Keywords: hunting cooperation; stochastic prey–predator model; nonlinear perturbation; stationary distribution; persistence in mean (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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