Impulsive delay differential inequality and stability of neural networks (Q1771384)

The authors consider a general Hopfield neural network with delays and fixed times of impulse effect and prove the global exponential stability of the trivial solution. The authors use the properties of \(M\)-cone and eigenspace of spectral radius of nonnegative matrices to prove a delay differential inequality of Halanay type with impulsive initial condition. Then, they apply such result to obtain an estimate for the exponential stability of the model. An example is given.