Global exponential stability of nonautonomous neural network models with unbounded delays

Abstract

For a nonautonomous class of n-dimensional differential system with infinite delays, we give sufficient conditions for its global exponential stability, without showing the existence of an equilibrium point, or a periodic solution, or an almost periodic solution. We apply our main result to several concrete neural network models, studied in the literature, and a comparison of results is given. Contrary to usual in the literature about neural networks, the assumption of bounded coefficients is not required to obtain the global exponential stability. Finally, we present numerical examples to illustrate the effectiveness of our results.

Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

“…Thus, combining (10), (21)-(25), we have Therefore, the method we used is more effective and general. Besides, we also extend some works about non-autonomous neural networks [13,22,43] to impulsive ones.…”

Global Exponential Stability and Periodicity of Nonautonomous Impulsive Neural Networks with Time‐Varying Delays and Reaction‐Diffusion Terms

“…In [27], the author improved some of the earlier Halanay-type inequalities and obtained the exponential stability of CNNs and the existence of periodic solutions through these new inequalities. In [28], sufficient conditions for the global exponential stability of a special class of nonautonomous differential systems with infinite time delay are given, without proving the existence of equilibrium point, periodic solution, or almost periodic solution. In addition, during the physical simulation of the neural network, the neural network will sometimes be interrupted due to the transient disturbance, which is called the impulse effect.…”

Approximation Results in Orlicz Spaces for Sequences of Kantorovich Max-Product Neural Network Operators

“…In conclusion, we recall that NN-type operators are usually based on certain density functions generated by sigmoidal functions. The latter fact is typical when one deal with NN type approximation processes, due to the biological reasons for which the neural networks have been introduced, see [34,38]. Examples of sigmoidal functions (see Section 3) are given, e.g., by the logistic function, the hyperbolic tangent function, and many others (see also [23]).…”