Analysis Of Autonomous Gilpin-Ayala Competition System With Random Perturbation

As we all know,the nature of any species is not isolated,they are always connected with each others.Represented by competition system,we establish the random competition,analy-sis changes of the system with random factors interfere,grasp the trend of the development of the population.Then,we can predict population development trend and provide theoretical reference for the corresponding control strategy.In this paper,we mainly prove that the randomized Gilpin-Ayala competition model has uniqueness positive solution.Meanwhile,we find the conditions of persistence,extinction and stationary distribution of randomized Gilpin-Ayala competition model.Besides,we also gives a numerical simulation to verify the correctness of the conclusions.Main results are as follows:By the nature of the solution of the Logistic model,we provide that the randomized Gilpin-Ayala competition model has uniqueness positive solution.(2)The randomized Gilpin-Ayala competition model was analyzed,then,we get the conditions of the persistence.By the method of the Lyapunov,we find the conditions of the stationary distribution of the randomized Gilpin-Ayala competition model.(4)We discussed the conditions of the extinction of the randomized Gilpin-Ayala competition model..(5)By Matlab,numerical simulations are carried out to support our results.