Analysis of a Class of Predation-Predation Model Dynamics with Random Perturbations

Xuewen Tan (), Pengpeng Liu, Wenhui Luo and Hui Chen
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Xuewen Tan: Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China
Pengpeng Liu: Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China
Wenhui Luo: Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China
Hui Chen: Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China

Mathematics, 2022, vol. 10, issue 18, 1-12

Abstract: In this paper, we study a class of predation–prey biological models with random perturbation. Firstly, the existence and uniqueness of systematic solutions can be proven according to Lipschitz conditions, and then we prove that the systematic solution exists globally. Moreover, the article discusses the long-term dynamical behavior of the model, which studies the stationary distribution and gradual properties of the system. Next, we use two different methods to give the conditions of population extinction. From what has been discussed above, we can safely draw the conclusion that our results are reasonable by using numerical simulation.

Keywords: random perturbation; Lipschitz conditions; stationary distribution; gradual properties; population extinction; numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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