Dynamical analysis on stochastic two-species models

Abstract

In this paper, we study three stochastic two-species models. We construct the stochastic models corresponding to its deterministic model by introducing stochastic noise into the equations. For the first model, we show that the system has a unique global solution starting from the positive initial value. In addition, we discuss the extinction and the existence of stationary distribution under some conditions. For the second system, we explore the existence and uniqueness of the solution. Then we obtain sufficient conditions for global asymptotic stability of the equilibrium point and the positive recurrence of solution. For the last model, the existence and uniqueness of solution, the sufficient conditions for extinction and asymptotic stability and the positive recurrence of solution and weak persistence are derived. And numerical simulations are performed to support our results.

Keywords:

• Stability
• extinction
• stationary distribution
• positive recurrence
• weak persistence

Mathematics Subject Classifications:

• 60G15
• 60G44
• 60G52
• 60H10

Disclosure statement

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

Additional information

Funding

This research was supported by Natural Science Foundation of Shandong Province, China [grant number ZR2020MA038] and [grant number ZR2020MA037].