Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense

Qiuyue Zhao () and Xinglong Niu
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Qiuyue Zhao: School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
Xinglong Niu: School of Electrical and Control Engineering, North University of China, Taiyuan 030051, China

Mathematics, 2024, vol. 12, issue 12, 1-14

Abstract: The random changes in the environment play a crucial role in the sustainability of ecosystems. Usually, the construction of stochastic models does not take into account the non-linear growth of intrinsic growth rate. In addition, prey only considers the collective response of the population when encountering predators and ignores the role of individual prey. To address this issue, we contemplate the dynamics of a stochastic prey–predator model with Smith growth rate and cooperative defense. The population density of prey is measured by mass, and the growth limitations are based on the proportion of unused available resources. Additionally, the grazing pattern of the predator incorporates cooperative characteristics into the functional response. We carry out existence and uniqueness analysis for the global positive solution. Then, we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solutions for investigating whether prey and predator populations continue to survive. Numerical examples indicate that the Smith growth rate, cooperative defense and environmental disturbance play crucial roles in the coexistence of interacting populations.

Keywords: Smith growth rate; cooperative defense; stochastic perturbation; stationary distribution; extinction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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