| There are three main types of interactions between species in nature,name-ly,competition,mutualistion and predation.Competition-competition-mutualist model plays an important role in building an ecological community.In recent decades,many scholars have conducted extensive research into the deterministic competition-competition-mutualist model,and obtained a lot of valuable research results.However,the parameters of the biological population model in the real world are inevitably affected by the external environment noises,and these noises are an important part of the ecosystem.Therefore,this makes the research on the biological population model with random disturbance become a prominent prob-lem,and has important practical application value.Based on this,we mainly study the dynamical properties of a class of competitive-competitive-mutualist model with random perturbations in this paper.Firstly,for the need of research,the local stability of the equilibrium points of the deterministic competitive-competitive-mutualist model is considered.Secondly,according to Ito's formula,and with the help of several important auxiliary lemmas,the persistence and extinction of the competition-competition-mutualist model with random perturbations are studied.The sufficient conditions for the extinction of three populations,the persistence of the single population,the persistence of t-wo populations and the persistence of three populations were established.Thirdly,based on Has'minskii theory,we discuss whether the stochastic model is stationary distribution and has a ergodic property,that is,the average of the number of popu-lations in time and the stationary distribution in space are equivalent in the sense of probability.Then,by constructing the appropriate Lyapunov function,it is proved that the positive equilibrium of the stochastic model is globally asymptotically sta-ble.Finally,we carry out some numerical simulations by using Matlab to illustract the main results in this paper. |
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