Work

The long-term dynamic behaviors of a stochastic predator-prey model with fear and group defense

Year: 2025

Type: article

Abstract: This paper analyzes a realistic predator-prey model accounting for the stochastic environment, fear and group defense in modeling. Employing stochastic analysis techniques such as ergodic theory, stochastic comparison theorem and occupation measure theory, we provide a group of sharp threshold-type conditions to characterize the long-term behaviors of this stochastic predator-prey model, including persistence, extinction, and the corresponding issues of ergodicity. When the population is persistent, we additionally give its ultimate stationary distribution. Furthermore, our results demonstrate that this stationary distribution can be effectively approximated by simulating the empirical measure of one sample path, which provides a convenient way for practical simulation and prediction. Our results reveal that excessive environment noise intensities will be detrimental to the survival of the prey and predator populations, whereas small environment noise intensities promote harmonious coexistence of the prey and predator populations.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2025166

Authors: Yuanping Cui, Shan Huang, Xiaoyue Li, Senyue Shi

Institutions: Tiangong University, Northeast Normal University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Tianjin City

Awards: G5207986968, G658636233, G7136063089