02159777

j

02159777 Xu, Daoyi Yang, Zhichun Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305, No. 1, 107-120 (2005). 2005 Elsevier, San Diego, CA EN delay differential equations impulse impulsive differential inequality neural networks stability

doi:10.1016/j.jmaa.2004.10.040

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. Marcia Federson (S\~ao Paulo)