The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic deriva...The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.展开更多
文章主要研究一类差分方程,其中aj>0,且ε是充分小的正常数,当1<sum from j=0 to ∞ aj=a<2和sum from j=0 to ∞ aj=a=∞时,通过构造李雅普诺夫函数的方法,根据李雅普诺夫稳定性定理,给出此差分方程在不同情况下解的渐近稳定...文章主要研究一类差分方程,其中aj>0,且ε是充分小的正常数,当1<sum from j=0 to ∞ aj=a<2和sum from j=0 to ∞ aj=a=∞时,通过构造李雅普诺夫函数的方法,根据李雅普诺夫稳定性定理,给出此差分方程在不同情况下解的渐近稳定性的充分条件。展开更多
基金supported by the National Natural Science Foundation of China(61273126)the Natural Science Foundation of Guangdong Province(10251064101000008+1 种基金S201210009675)the Fundamental Research Funds for the Central Universities(2012ZM0059)
文摘The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.
