A Class of Jellyfish Model with Ornstein-Uhlenbeck Process
LIANG Chunye
WANG Qinglong
GUO Yuhong
LIU Zhijun
Abstract：With the idea of environmental noises,a jellyfish model perturbed by the Ornstein-Uhlenbeck process was developed to investigate the effects of random perturbations on the dynamic behavior of jellyfish populations.Firstly,global solution of the model was analyzed and sufficient condition for the extinction of jellyfish was given by the Lyapunov function method.Secondly,by using the Khasminskii theory,sufficient condition for the existence of the stationary distribution of the model was obtained.Finally,several specific numerical examples were employed to validate the theoretical findings.The results indicate that the increasing of the speed of reversion or the decreasing of the intensity of volatility can both accelerate the extinction rate of jellyfish populations,which means that the growth of jellyfish populations can be controlled by appropriately adjusting the magnitude of the speed of reversion or the intensity of volatility.The proposed model provides some theoretical results for designing control strategies for jellyfish outbreaks.
Keywords：stochastic jellyfish modelOrnstein-Uhlenbeck processLyapunov function methodKhasminskii theoryextinctionstationary distribution
Publication Date：2024-06-20
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：9( 267-275 )