Adaptive synchronization for fractional stochastic neural network with delay

Lu Junxiang,Hong Xue

doi:10.1186/s13662-020-03170-2

Abstract

Under the Brownian motion environment, adaptive synchronization is mainly studied in this paper for fractional-order stochastic neural networks (FSNNs) with time delays and discontinuous activation functions. Firstly, an existence theorem of solutions is established and global solutions of FNNs are obtained under the definition of Filippov solution by using the fixed-point theorem for a condensing map. Secondly, an adaptive controller is designed to ensure the synchronization between FNNs and the corresponding fractional-order FSNNs. Finally, a numerical example is given to illustrate the given results.

Highlights

The fractional-order systems and fractional calculus have attracted many researchers’ attention
The fractional-order systems and fractional calculus have been applied to neural networks recently to establish the fractional-order neural networks system (FNNs)
Motivated by the above discussion, we mainly investigate the adaptive synchronization for the fractional-order NNs with time delays and discontinuous activation functions under the Brownian motion environment in this paper

Summary

Introduction

The fractional-order systems and fractional calculus have attracted many researchers’ attention. The dynamic characteristics for FNNs attracted some researchers, see, e.g., [6,7,8,9,10,11], and in particular the synchronization, which is one of the most important dynamic characteristics for these systems, has seen more and more interesting applications in information fields. Most recently the authors of [15,16,17,18] have studied the adaptive synchronization for fractionalorder NNs under the assumption that the activation functions are generally Lipschitz continuous. The synchronization criteria of neural systems mainly take into account the Lyapunov stability theory, picking the L–K functional, and investigating its derivative with the appropriate methodologies. It is a challenge to pick an appropriate L–K functional for a fractional-order system

Objectives

Conclusion