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研究以竞争微分方程为模型的动态系统,它总结了长期和短期记忆两个方面的动态行为特征。这种神经网络的行为以一个表征快速变化现象的神经活动方程,和一个表征神经系统的慢速变化的动态调整方程来刻画。应用M-矩阵与Lyapunov稳定性理论,分析具有不同时间尺度的生物动态神经网络的指数稳定性,给出保证此神经网络平衡点全局存在唯一且指数稳定的一个充分条件,和一定条件下的一个充要条件。
The dynamic system, which takes the competition differential equation as a model, is studied, which summarizes the dynamic behavioral characteristics of both long-term and short-term memory. The behavior of this neural network is characterized by a neural activity equation that characterizes rapid changes and a dynamic adjustment equation that characterizes slow changes in the nervous system. By using the theory of M-matrix and Lyapunov stability, the exponential stability of bio-dynamic neural networks with different time scales is analyzed. A sufficient and sufficient condition for guaranteeing that the equilibrium point of the neural network exists globally and exponentially is given. Under certain conditions, Necessary and Sufficient Condition.