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Impulsive delay differential inequality and stability of neural networks. (English) Zbl 1091.34046

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.

MSC:

34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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