Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks

Marat Akhmet,Madina Tleubergenova,Zakhira Nugayeva

doi:10.3390/math8101791

Abstract

In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincaré chaos. Thus, the importance of the dynamics is indisputable for those problems of artificial intelligence, brain activity and robotics, which rely on chaos. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable solutions are determined. The oscillations continue the line of periodic and almost periodic motions, which already are verified as effective instruments of analysis and applications for image recognition, information processing and other areas of neuroscience. The concept of strongly unpredictable oscillations is a significant novelty of the present research, since the presence of chaos in each coordinate of the space state provides new opportunities in applications. Additionally to the theoretical analysis, we have provided strong simulation arguments, considering that all of the assumed conditions are fulfilled.

Highlights

IntroductionThe Hopfield type neural networks were first developed in 1982 [1], through establishing the connection of neural networks with physical systems considered in statistical mechanics [2]
The Hopfield type neural networks were first developed in 1982 [1], through establishing the connection of neural networks with physical systems considered in statistical mechanics [2].Hopfield neural network is an artificial neural network for storing and retrieving memory similar to the human brain
This is the first time that the Hopfield-type neural networks are considered for existence, uniqueness and asymptotic stability of unpredictable oscillations

Summary

Introduction

The Hopfield type neural networks were first developed in 1982 [1], through establishing the connection of neural networks with physical systems considered in statistical mechanics [2]. A new type of oscillations, which are described by unpredictable functions, was introduced in [32] It relies on the dynamics of unpredictable points and Poincaré chaos [33]. We have designed the new model of Hopfield type neural networks with unpredictable perturbations and derive sufficient conditions of the existence, uniqueness, and asymptotic stability of the strongly unpredictable oscillations, which develop previously known results in [3,4,5,6,7,8,9,10], and others. The main results of the present study are placed, where the existence, uniqueness and stability of strongly unpredictable oscillations of Hopfield-type neural networks systems are investigated.

Preliminaries

Main Results

Examples

Conclusions