This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From th...This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.展开更多
In this paper, we introduce the stochasticity into an HIV-1 infection model with cytotoxic T lymphocytes （CTLs） immune response via the technique of parameter perturbation. We show that there is a positive solution ...In this paper, we introduce the stochasticity into an HIV-1 infection model with cytotoxic T lymphocytes （CTLs） immune response via the technique of parameter perturbation. We show that there is a positive solution as desired in any population dynamics. Then we analyze the long time behavior of this model. We obtain a sufficient condition for the stochastic asymptotic stability in the large of the infection-free equilibrium and give the conditions for the solution fluctuating around the two infection equilibria （one without CTLs being activated and the other with）. Finally, we make sinmlations to conform to our analytical results.展开更多
In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded m...In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded mean of solution is obtained by using the Liyapunov function and Chebyshev inequality. Lastly, stochastic global asymptotic stability of zero equilibriums is analyzed.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10902085)
文摘This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.
基金We would like to thank the editor and referee for their very helpful comments and suggestions. We also thank the National Natural Science Foundation of China （No. 10971021）, the Ministry of Education of China （No. 109051）, the Ph.D. Pro- grams Foundation of Ministry of China （No. 200918） and the Graduate Innovative Research Project of NENU （No. 09SSXTl17） for their financial support.
文摘In this paper, we introduce the stochasticity into an HIV-1 infection model with cytotoxic T lymphocytes （CTLs） immune response via the technique of parameter perturbation. We show that there is a positive solution as desired in any population dynamics. Then we analyze the long time behavior of this model. We obtain a sufficient condition for the stochastic asymptotic stability in the large of the infection-free equilibrium and give the conditions for the solution fluctuating around the two infection equilibria （one without CTLs being activated and the other with）. Finally, we make sinmlations to conform to our analytical results.
基金supported by the National Natural Sciences Foundation of China(11371313)the Sciences Foundation of Yuncheng University(XK2012003)
文摘In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded mean of solution is obtained by using the Liyapunov function and Chebyshev inequality. Lastly, stochastic global asymptotic stability of zero equilibriums is analyzed.
