The Dynamics of Stochastic Predator-Prey Models with Non-Constant Mortality Rate and General Nonlinear Functional Response
Year: 2020
Author: Hao Peng, Xinhong Zhang
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 4 : pp. 495–511
Abstract
In this paper, we investigate the dynamics of stochastic predator-prey models with non-constant mortality rate and general nonlinear functional response. For the stochastic system, we firstly prove the existence of the global unique positive solution. Secondly, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing an appropriate Lyapunov function, we prove that there exists a unique stationary distribution and it has ergodicity in the case of persistence. Finally, numerical simulations are introduced to illustrate our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2020.495
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 4 : pp. 495–511
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Stochastic predator-prey model Non-constant mortality rate General nonlinear functional response Extinction Stationary distribution.