Stability analysis for delayed high-order type of Hopfield neural networks with impulses

This paper can be regarded as the continuation of the work of the authors contained in papers (2015). At the same time, it represents the extension of the papers Lou and Cui (2007, [24]), Sannay (2007, [34]) and Acka et al. (2004, [1]). This work discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. By utilizing Lyapunov functional method and the linear inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. The exponential convergence rate of the equilibrium point is also estimated. Finally, we analyze and interpret four numerical examples proving the efficiency of our theoretical results and showing that impulse can be used to stabilize and exponentially stabilize some high-order Hopfield-type neural networks.