Dynamic Analysis Of Several Stochastic New Logistic Models

In this paper,based on the New Logistic model,for the single population case,the stochastic New Logistic model,the stochastic New Logistic model with impulse perturbation and the stochastic New Logistic model with finite Markov chain and Lévy noise are established;for the case of two populations,taking into account the effect of white noise,a stochastic LV extended New Logistic model is proposed.And the dynamical properties of each model are studied.Firstly,for the stochastic New Logistic model,the existence and uniqueness of the global positive solution of the system is proved by contradiction.The weak persistence of the system is given by the strong law of large numbers for local martingales.The stochastic persistence is proved by Chebyshev inequality.Secondly,for the stochastic New Logistic model with impulsive perturbation,the existence and uniqueness of the global positive solution of the system is proved by using the equivalence method,and the weak persistence and stochastic persistence of the system are analyzed.Studies have shown that the impulse has an important effect on the growth of the population,the positive coefficient of the impulse effect is beneficial for the growth of the population,while the negative impulse effect inhibits the growth of the microbial population.Thirdly,for the stochastic New Logistic model with finite Markov chain and Lévy noise,the existence and uniqueness of the global positive solution of the system is proved.The weak persistence of the system is proved by the strong law of large numbers and ergodic theory.The stochastic persistence of the system is proved by the generalized It(?) formula and M-matrix theory.Finally,for the stochastic LV extended New Logistic model,the existence and uniqueness of the global positive solution of the system is proved.The stochastic ultimate boundedness is proved by constructing Lyapunov function and Chebyshev inequality,and the asymptotic moment estimation of the solution in system is given.