## Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations.(English)Zbl 1163.92308

Summary: This paper introduces a new class of functions, called inverse Lipschitz functions $$(i \mathcal L)$$. By using $$i \mathcal L$$, a novel class of neural networks with inverse Lipschitz neuron activation functions is presented. By topological degree theory and matrix inequality techniques, the existence and uniqueness of equilibrium points for the neural network are investigated. By constructing appropriate Lyapunov functions, a sufficient condition ensuring global exponential stability of the neural network is given. At last, two numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.

### MSC:

 92B20 Neural networks for/in biological studies, artificial life and related topics 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations

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### References:

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