A nonlinear version of the distributed Halanay inequality and its application
Nasser‐eddine Tatar, Rathinasamy Sakthivel · Mathematical Methods in the Applied Sciences · 2021
In this paper, first we prove a nonlinear version of Halanay inequality with distributed delay. Then, we use it to establish a local exponential stability result for a problem appearing in neural networks theory under the name Hopfield neural network system. This is done for activation functions violating the usual standard condition of Lipschitz continuity. One of the activation functions may be non‐Lipschitz continuous. Finally, an example is provided to illustrate the developed theory.