Journal
APPLIED MATHEMATICS LETTERS
Volume 112, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2020.106756
Keywords
Stochastic predator-prey model; Fear effect; Nonlinear perturbation; Stationary distribution; Ergodicity
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Funding
- National Natural Science Foundation of China [11871473]
- Shandong Provincial Natural Science Foundation, China [ZR2019MA010]
- Fundamental Research Funds for the Central Universities, China [2412020QD024]
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In this paper, a stochastic predator-prey system is constructed and analyzed, with criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions established using suitable Lyapunov functions. The existence of a stationary distribution indicates long-term persistence and coexistence of both prey and predator species.
In this paper, we construct and analyze a stochastic predator-prey system where apart from direct predation the prey population is affected by the fear induced from predators. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological interpretation, the existence of a stationary distribution indicates that both the prey and predator species will be persistent and coexistent in the long term. (c) 2020 Elsevier Ltd. All rights reserved.
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