Extinction and strong persistence in the Beddington–DeAngelis predator–prey random model

This paper studies a predator–prey model with a Beddington–DeAngelis type functional response under the stationary Ornstein–Uhlenback process. First, we prove the existence and uniqueness of the global positive solution for the given system for any initial datum. Second, we turn to its internal stru...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 46; no. 18; pp. 19351 - 19363
Main Authors Zhu, Huijian, Li, Lijie, Pan, Weiquan
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.12.2023
Subjects
Mathematical models
Predator-prey simulation
Predators
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Summary:This paper studies a predator–prey model with a Beddington–DeAngelis type functional response under the stationary Ornstein–Uhlenback process. First, we prove the existence and uniqueness of the global positive solution for the given system for any initial datum. Second, we turn to its internal structures and establish the existence of a compact forward‐absorbing set as well as a forward attracting one. Finally, we carry out some numerical simulations to support the theoretical results.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9629