混杂型离散时间脉冲时滞Hopfield神经网络的多稳定性分析

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。

Multistability Analysis of Hybrid Discrete-time Impulsive Hopfield-type Neural Networks with Delays

The multistability problem of a class of hybrid discrete-time impulsive Hopfield-type neural networks with delays is studied. First, by applying Brouwer fixed point theorem, it is proved that the impulsive delayed neural networks under consideration possess multiple equilibriums. Then a Lyapunov function based method combined with inequality based analysis techniques is developed to establish a criterion for multistability of hybrid impulsive discrete-time Hopfield-type neural 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.