Dynamic Behavior Of Stochastic Delayed System And Its Applications

Due to the extensive applications of stochastic delayed system in aerospace, en-gineering.industrial control,financial economics and so on. the dynamic behavior of stochastic delayed system have been became one of the hot spots in today’s world. The paper is concerned with the dynamic behavior of several class stochastic delayed sys-tem, including:stochastic differential-integro equation, stochastic Cohen-Grossberg neu-ral networks, stochastic time-varying delayed cellular neural networks, stochastic delayed bidirectional associative memory (BAM) neural networks with reaction diffusion terms, and its application on synchronization. The main comments include the followings:1. Two classes of stochastic differential-integro equations with S-type distributed delays are considered. By constructing l-operator differential inequality and applying Holder inequality and stochastic analysis technique, the sufficient conditions to ensure pth moment exponential stability of zero solution for one equation are given. And by nonnegative semimartingale convergence theorem and linear matrix inequality(LMI). the sufficient condition to ensure almost surely exponential stability for another equation is obtained.2. Stochastic fuzzy Cohen-Grossberg neural networks with time-varying delays is considered. Without the boundness of activation function, by applying homeomorphism theory, constructing Lyapunov function and using inequality technique, some sufficient criteria to ensure the existence, uniqueness and globally exponential stability for the equi-librium point of deterministic system and the existence, uniqueness and pth moment expo-nential stability for the equilibrium point of stochastic system are obtained; And, stochas-tic Cohen-Grossberg neural networks with continuously distributed delays is also stud-ied. By applying the method of variation parameter and using inequality techniques and stochastic analysis methods, some sufficient conditions ensuring pth moment exponential stability of stochastic Cohen-Grossberg neural networks are given; Furthermore, by the same method, the synchronization of stochastic Cohen-Grossberg neural networks with S-distributed delays is considered and some sufficient conditions ensuring pth moment exponential synchronization are obtained.3. By constructing different Lyapunov functions and employing the nonnegative semimartingale convergence theorem, we discuss stochastic fuzzy cellular neural net-works with time-varying delays and two independent sufficient criteria ensuring almost sure exponential stability of the networks are given:Furthermore, without the differentia-bility of the delay functions, by using variation parameter approach and stochastic analy-sis methods, the result to ensure the almost sure exponential stability of stochastic cellular neural networks with time-vary ing delays was gotten.4. Stochastic delayed BAM neural networks with reaction diffusion terms is con-sidered. By applying the nonnegative semimartingale convergence theorem and using in-equality technique and stochastic analysis methods, some sufficient conditions to ensure almost sure exponential stability and mean square stability of stochastic delayed BAM neural networks with reaction diffusion terms are obtained.