随机时滞系统的动力学行为及其应用
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摘要
由于随机时滞系统在航空航天、工程技术、工业控制、金融经济等领域的广泛应用,随机时滞系统的动力学行为已经成为当今世界的研究热点问题之一.本文研究了几类随机时滞系统：随机微分积分方程,随机LCohen-Grossberg神经网络,随机变时滞递归神经网络,随机时滞反应扩散神经网络的动力学行为,及其在同步问题中的应用.主要研究内容包括：
1.研究了两类具有S-分布时滞的随机微分积分方程的动力学行为.通过建立(?)-算子微分不等式和利用Holder不等式及随机分析技巧,得到了一类方程零解p阶矩指数稳定的充分条件,并将结果应用于神经网络模型,得到了随机细胞神经网络零解p阶矩指数稳定的充分条件；通过运用非负半鞅收敛定理和线性矩阵不等式,得到了另一类随机微分积分方程零解几乎确定指数稳定的充分条件.
2.研究了随机模糊变时滞Cohen-Grossberg神经网络.通过利用同胚映射定理,构造合适的李雅普诺夫函数和运用不等式技巧,在不需要激活函数有界的条件下,得到了确定系统平衡点存在唯一和全局指数稳定以及随机系统平衡点存在唯一和p阶矩指数稳定的充分条件；此外,我们还讨论了具有连续分布时滞的随机Cohen-Grossberg神经网络.通过运用常数变易法、不等式技巧和随机分析方法,得到了具有连续分布时滞的随机Cohen-Grossberg神经网络p阶矩指数稳定的充分条件；并且,我们将此方法应用于具有S-分布时滞的随机Cohen-Grossberg神经网络的同步问题,得到了具有S-分布时滞的随机Cohen-Grossberg神经网络p阶矩指数同步的充分条件.
3.通过建立不同的李雅普诺夫函数和运用非负半鞅收敛定理,研究了随机模糊变时滞细胞神经网络的几乎确定指数稳定性,获得了此类神经网络平衡点几乎确定指数稳定的两个相互独立的充分条件；进一步,在不需要时滞函数可微的条件下,利用常数变易法和随机分析的方法,获得了一类随机变时滞细胞神经网络几乎确定指数稳定的充分条件.
4.研究了随机时滞反应扩散BAM神经网络的动力学行为.通过利用非负半鞅收敛定理以及运用不等式技巧和随机分析法方法,得到了随机时滞反应扩散BAM神经网络几乎确定指数稳定和均方稳定的充分条件.
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.
1.研究了两类具有S-分布时滞的随机微分积分方程的动力学行为.通过建立(?)-算子微分不等式和利用Holder不等式及随机分析技巧,得到了一类方程零解p阶矩指数稳定的充分条件,并将结果应用于神经网络模型,得到了随机细胞神经网络零解p阶矩指数稳定的充分条件；通过运用非负半鞅收敛定理和线性矩阵不等式,得到了另一类随机微分积分方程零解几乎确定指数稳定的充分条件.
2.研究了随机模糊变时滞Cohen-Grossberg神经网络.通过利用同胚映射定理,构造合适的李雅普诺夫函数和运用不等式技巧,在不需要激活函数有界的条件下,得到了确定系统平衡点存在唯一和全局指数稳定以及随机系统平衡点存在唯一和p阶矩指数稳定的充分条件；此外,我们还讨论了具有连续分布时滞的随机Cohen-Grossberg神经网络.通过运用常数变易法、不等式技巧和随机分析方法,得到了具有连续分布时滞的随机Cohen-Grossberg神经网络p阶矩指数稳定的充分条件；并且,我们将此方法应用于具有S-分布时滞的随机Cohen-Grossberg神经网络的同步问题,得到了具有S-分布时滞的随机Cohen-Grossberg神经网络p阶矩指数同步的充分条件.
3.通过建立不同的李雅普诺夫函数和运用非负半鞅收敛定理,研究了随机模糊变时滞细胞神经网络的几乎确定指数稳定性,获得了此类神经网络平衡点几乎确定指数稳定的两个相互独立的充分条件；进一步,在不需要时滞函数可微的条件下,利用常数变易法和随机分析的方法,获得了一类随机变时滞细胞神经网络几乎确定指数稳定的充分条件.
4.研究了随机时滞反应扩散BAM神经网络的动力学行为.通过利用非负半鞅收敛定理以及运用不等式技巧和随机分析法方法,得到了随机时滞反应扩散BAM神经网络几乎确定指数稳定和均方稳定的充分条件.
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.
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