一类具有连续分布延时的随机反应扩散的Hopfield神经网络的收敛动力学行为  

CONVERGENCE DYNAMICS OF STOCHASTIC REACTION-DIFFUSION HOPFIELD NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

作　　者：戴志娟[1] 孙建华[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《南京大学学报（数学半年刊）》2005年第2期197-211,共15页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：本文研究了一类具有连续分布延时的随机反应扩散的神经网络模型.通过构建恰当的Lyapunov函数,以及运用非负半鞅收敛性定理,得到了该网络平衡解几乎必然指数稳定和矩指数稳定的充分条件.最后我们给出了一个例子验证了条件的正确性.本文所得到的结果不要求激励函数是可导,有界,单调非减的,也不要求连接权矩阵是对称的,在解决最优化问题等方面有重要意义.因此我们推广和完善了以前的结果.Stochastic effects to convergence dynamics of reaction-diffusion Hopfieldneural networks （RDHNNs） with continuously distributed delays are studied. Withoutassuming the boundedness, monotonicity and differentiability of the activation func-tions and the symmetry of synaptic interconnection weights, by constructing suitableLyapunov functionals and employing nonnegative semimartingale convergence theorem,delay independent and easily verifiable sufficient conditions to guarantee the almost sureexponential stability and p-th moment exponential stability of an equilibrium solutionassociated with temporally uniform external inputs to the networks are obtained. Oneexample is also given to demonstrate our results.

关 键 词：HOPFIELD神经网络 反应扩散 时滞 非负半鞅收敛定理 几乎必然指数稳定 

分 类 号：O175[理学—数学]