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.
Highlights
As we all know, the classical Lotka–Volterra model can well describe the competition among different populations, it has been one of the most important models in the field of mathematical ecology
6 Numerical examples we demonstrate the efficiency of the proposed condition of permanence and extinction with some illustrative examples
7 Conclusion From a biological point of view, it is an interesting topic to consider the survival of the resource competition system with stochastic surrounding noises
Summary
The classical Lotka–Volterra model can well describe the competition among different populations, it has been one of the most important models in the field of mathematical ecology. Based on Tillman’s theory, scholars proposed a new method that predicted the final competition results by using resource requirement among competing populations.
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