A PREDATOR–PREY MODEL IN A STOCHASTIC ENVIRONMENT WITH PREDATOR MIGRATION

Ao Shen, Yuming Chen and Li Wang
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Ao Shen: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, P. R. China
Yuming Chen: ��Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada
Li Wang: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 01, 1-19

Abstract: In this work, a predator–prey model is considered to study its dynamics in a stochastic environment with the addition of predator migration. First, conditions on the existence of positive equilibria, along with their stability, and the emergence of limit cycles in the corresponding deterministic system are derived. Then, two stochastic properties are established: The ultimate boundedness of solutions and the existence of an ergodic stationary distribution for the system under consideration. The theoretical results are supported by numerical simulations, which reveal the significant influence of migration on the dynamical behaviors of both deterministic and stochastic systems.

Keywords: Predator–Prey Model; Migration; White Noise; Ergodic Stationary Distribution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500252

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