A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments

Yuanfu Shao () and Weili Kong
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Yuanfu Shao: School of Science, Guilin University of Technology, Guilin 541004, China
Weili Kong: School of Teacher Education, Qujing Normal University, Qujing 655011, China

Mathematics, 2022, vol. 10, issue 18, 1-25

Abstract: In view of prey’s delayed fear due to predators, delayed predator gestation, and the significance of intra-specific competition between predators when their populations are sufficiently large, a prey–predator population model with a density-dependent functional response is established in a deterministic environment. We research the existence and asymptotic stability of the equilibrium statuses. Then, taking into consideration environmental disturbances, we extend the deterministic model to a stochastic model and research the existence and stationary distributions of stochastic solutions. Finally, we perform some numerical simulations to verify the theoretical results. Numerical examples indicate that fear, delays and environmental disturbance play crucial roles in the system stability of the equilibrium status.

Keywords: multi-time delay; fear of predator; equilibrium status; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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