A stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process

Abstract

In this paper, a stochastic predator–prey model with two competitive preys and Ornstein–Uhlenbeck process is formulated and analysed, which is used to obtain a better understanding of the population dynamics. At first, we validate that the stochastic system has a unique global solution with any initial value. Then we analyse the stochastic dynamics of the model in detail, including pth moment boundedness, asymptotic pathwise estimation in turn. After that, we obtain sufficient conditions for the existence of a stationary distribution of the system by adopting stochastic Lyapunov function methods. In addition, under some mild conditions, we derive the specific form of covariance matrix in the probability density near the quasi-positive equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings.

Keywords:

• Three-species predator–prey model
• competition between preys
• ornstein–Uhlenbeck process
• moment boundedness
• stationary distribution
• density function

Acknowledgments

The author read and approved the final manuscript.

Availability of data and materials

Data sharing is not applicable to this article as no datasets are generated or analysed during the current study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author thanks the National Natural Science Foundation of P.R. China [grant number 12001090] and the Jilin Provincial Science and Technology Development Plan Project [grant number YDZJ202201ZYTS633].