POPULATION DYNAMICAL BEHAVIORS OF JELLYFISH MODEL WITH RANDOM PERTURBATION

We are interested in modeling the influence of random fluctuations on population systems. In this paper, we consider the population dynamics of jellyfish stochastic differential equation by introducing the random perturbation. Firstly, we provide the sufficient criteria to study the existence and uniqueness of non-negative solution. We prove that population will be permanence and persistence in mean when the noise is relatively small as well as it is discussed that the population may become extinct with probability one when the noise is too large. Then we show that the system has a stationary distribution under sufficient conditions using Hasminskii’s methods and Lyapunov function. Finally, numerical simulations are performed to verify the results attained in this paper.