Permanence and extinction of a high-dimensional stochastic resource competition model with noise

Abstract

Abstract In this paper, we investigate the asymptotic behavior for a kind of resource competition model with environmental noises. Considering the impact of white noise on birth rate and death rate separately, we first prove the existence of a positive solution, and then a sufficient condition to maintain permanence and extinction is obtained by using a proper Lyapunov functional, stochastic comparison theorem, strong law of large numbers for martingales, and several important inequalities. Furthermore, the stochastic final boundedness and path estimation are studied. Finally, the fact that the intensity of white noise has a very important influence on the permanence and extinction of the system’s solution is illustrated by some numerical examples.

Keywords

• Permanence and extinction
• Lyapunov functional
• Stochastic comparison theorem
• Strong number theorem of martingale