Coexistence for a kind of stochastic three-species competitive models

Abstract

The coexistence of species sustains the ecological balance in nature. This paper focuses on sufficient conditions for the coexistence of a three-species stochastic competitive model, where the model has non-linear diffusion parts. Three values λ3z, λ3x and λ3y are introduced and calculated from the coefficients, which can be considered as threshold values. Moreover, convergence in distribution of the positive solution of the model is also addressed. A few numerical simulations are carried out to illustrate the theoretical results.

Keywords

• three-species competitive model
• coexistence
• environmental noise
• non-linear diffusion
• ergodicity
• 60h10
• 60j70
• 92d25
• 93d15