脉冲高阶时滞Hopfield型神经网络的稳定性分析

Stability analysis of impulsive high-order Hopfield-type neural networks with delays

针对进化过程中顺序的突然改变导致无法用纯连续或纯粹的离散神经网络来描述的问题,给出了脉冲高阶时滞Hopfield型神经网络模型,并得到时滞脉冲系统渐近稳定的结果.然后,利用该结果和李亚普诺夫方法以及数学分析技术分析网络的稳定性.在激励函数连续、单调有界的条件下,给出了保证脉冲高阶时滞Hopfield型神经网络全局一致渐近稳定的充分条件.这些条件含有许多可调参数,为神经网络提供灵活的设计与分析;并且易于检验,适用于分析生物神经系统的动态特性或设计全局稳定的神经网络.最后,通过仿真实例说明了所得结果的有效性.

Aiming at the problem that the evolutionary processes which have sequential abrupt changes cannot be appropriately described by pure continuous or pure discrete neural network model,a model of impulsive high-order Hopfield type neural networks with delays is formulated.And a result for the asymptotic stability of impulsive systems with delays is given.By using this result,the Lyapunov method and mathematical analysis techniques,the stability of the networks is analyzed.The sufficient conditions guaranteeing the global uniform asymptotic stability of the networks are given under the conditions that the activation functions are continuous,monotonous and bounded.Many adjustable parameters are introduced in the criteria,providing flexibility for the design and analysis of the networks.The criteria are easily verified and can be used to analyze the dynamics of biological neural systems or to design globally stable artificial neural networks.Finally,an example is given to demonstrate the effectiveness of the obtained results.