Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks.

Gani Stamov,Ivanka Stamova,Anatoliy Martynyuk,Trayan Stamov

doi:10.3390/e22030337

Abstract

In this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.

Highlights

Cellular neural network systems [1,2] and their various generalizations have attracted the attention of the researchers due to their incredible opportunities for applications in areas such as pattern recognition, associative memory, classification, parallel computation, as well as, their ability to solve complex optimization problems
In numerous cases the model can be unstable in the classical Lyapunov’s sense, but its performance may be sufficient for the practical point of view. For such situations, when the dynamic of systems contained within particular bounds during a fixed time interval, the researchers introduced the notion of practical stability [54,55,56,57]
With this research we extend the results on impulsive neural network Hopfield-type models to the fractional-like case

Summary

Introduction

Cellular neural network systems [1,2] and their various generalizations have attracted the attention of the researchers due to their incredible opportunities for applications in areas such as pattern recognition, associative memory, classification, parallel computation, as well as, their ability to solve complex optimization problems. In numerous cases the model can be unstable in the classical Lyapunov’s sense, but its performance may be sufficient for the practical point of view For such situations, when the dynamic of systems contained within particular bounds during a fixed time interval, the researchers introduced the notion of practical stability [54,55,56,57]. To the best of the authors’ knowledge, practical stability results have not been derived for impulsive fractional-like neural network systems. We will consider the practical stability properties of the designed neural network model with FLDs with respect to manifolds [60,61,62].

Generalized FLDs and Integrals

Impulsive Fractional-Like Neural Networks

Main Practical Stability Results

The constants Qik and Tjk are such that

Impulsive Fractional-Like Neural Networks with Uncertain Parameters

Conclusions