混杂型离散时间脉冲时滞 Hopfield神经网络的多稳定性分析

摘要

The multistability problem of a class of hybrid discrete-time impulsive Hopfield-type neural networks with de-lays is studied.First,by applying Brouwer fixed point theorem,it is proved that the impulsive delayed neural networks un-der consideration possess multiple equilibriums.Then a Lyapunov function based method combined with inequality based a-nalysis techniques is developed to establish a criterion for multistability of hybrid impulsive discrete-time Hopfield-type neu-ral networks with multiple equilibriums.Additionally,the estimates on the domains of attraction of stable equilibriums are provided.Finally,a numerical example is given to illustrate the effectiveness of the derived results.%研究一类混杂型离散时间脉冲时滞 Hopfield神经网络的多稳定性问题。首先，运用 Brouwer不动点定理，证明所考虑的脉冲时滞神经网络具有多个平衡点。然后，引入Lyapunov函数，运用不等式分析技术，建立脉冲离散时滞 Hopfield神经网络多稳定性判别准则，并给出平衡点吸引域的估计。最后，通过数值实例仿真验证结果的有效性。