Finite-Time Projective Synchronization of Fractional-Order Memristive Neural Networks with Mixed Time-Varying Delays

Meng Hui,Herbert Ho-Ching Iu,Chen Wei,Lin Bai,Ni Luo,Jiao Zhang,Rui Yao

doi:10.1155/2020/4168705

Abstract

This paper is concerned with the finite-time projective synchronization problem of fractional-order memristive neural networks (FMNNs) with mixed time-varying delays. Firstly, under the frame of fractional-order differential inclusion and the set-valued map, several criteria are derived to ensure finite-time projective synchronization of FMNNs. Meanwhile, three properties are established to deal with different forms of the finite-time fractional differential inequation, which greatly extend some results on estimation of settling time of FMNNs. In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

Highlights

In the past several decades, artificial neural networks have been extensively investigated due to their wide applications in signal processing [1], combinatorial optimization [2], pattern recognition [3], associative memories [4], and so on
It is well known that time delays are unavoidable in neural networks
On the other hand, distributed time delays should be considered in neural networks because neural networks usually have a spatial nature and the presence of a large number of parallel pathways with multifarious axon sizes and lengths [8]

Summary

Introduction

In the past several decades, artificial neural networks have been extensively investigated due to their wide applications in signal processing [1], combinatorial optimization [2], pattern recognition [3], associative memories [4], and so on. In [27], by using the Gronwall–Bellman integral inequality and the Volterra integral equation, the authors explored the finite-time projective synchronization problem of memristor-based delay fractional-order neural networks. . Zhang and Deng studied the finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks with time delays in [28]. Inspired by the above discussion, this paper will study the finite-time projective synchronization of FMNNs with mixed time-varying delays via applying differential inequality of the Caputo derivative and the asymptotic expansion property of Mittag-Leffler function. In the aV(t) − existing b or literature studies on finite-time synchronization of fractional-order neural networks, most pay attention to discuss the synchronization condition a ≥ 0 and ignore the computation of settling time. Euler’s gamma function which is defined by Γ(α) 􏽒+0∞ sα− 1e− s ds

Preliminaries and Model Description

Main Results

Numerical Simulation

Conclusion