In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linea...In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.展开更多
Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approxi...Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.展开更多
So far there have been few results presented on the exponential stability for time-changed stochastic differential equations.The main aim of this work is to fill this gap.By making use of general Lyapunov methods and ...So far there have been few results presented on the exponential stability for time-changed stochastic differential equations.The main aim of this work is to fill this gap.By making use of general Lyapunov methods and time-changed Itôformula,we establish the exponential stability and almost sure exponential stability of solution to time-changed SDEs.Finally,we construct some examples to illustrate the effectiveness of our established theory.展开更多
The stability of stochastic delayed cellular neural networks(DCNNs) is investigated in this paper. Under the help of Lyapunov functional and the semimartingale convergence theorem, some sufficient criteria were obtain...The stability of stochastic delayed cellular neural networks(DCNNs) is investigated in this paper. Under the help of Lyapunov functional and the semimartingale convergence theorem, some sufficient criteria were obtained to check the almost sure exponential stability of the DCNNs.展开更多
In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems ar...In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.展开更多
基金the National Natural Science Foundation of China (No. 10571036)Tianjin Municipal Education Commission of China(No. 20070405)
文摘In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.
文摘Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
基金by the National Natural Science Foundation of China(Nos.11901188,61703001)by the Scientific Research Funds of Hunan Provincial Education Department of China(No.19B156).
文摘So far there have been few results presented on the exponential stability for time-changed stochastic differential equations.The main aim of this work is to fill this gap.By making use of general Lyapunov methods and time-changed Itôformula,we establish the exponential stability and almost sure exponential stability of solution to time-changed SDEs.Finally,we construct some examples to illustrate the effectiveness of our established theory.
基金Sponsored by the National Natural Science Foundation of China (Grant No.10171009) and the Natural Science Foundation of Heilongjiang Province(Grant No.A200605).
文摘The stability of stochastic delayed cellular neural networks(DCNNs) is investigated in this paper. Under the help of Lyapunov functional and the semimartingale convergence theorem, some sufficient criteria were obtained to check the almost sure exponential stability of the DCNNs.
基金Supported by the National Natural Science Foundation of China under Grant 10461001.
文摘In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.
