Asymptotic Stability and Asymptotic Synchronization of Memristive Regulatory-Type Networks

Jin-E Zhang

doi:10.1155/2017/4538230

Abstract

Memristive regulatory-type networks are recently emerging as a potential successor to traditional complementary resistive switch models. Qualitative analysis is useful in designing and synthesizing memristive regulatory-type networks. In this paper, we propose several succinct criteria to ensure global asymptotic stability and global asymptotic synchronization for a general class of memristive regulatory-type networks. The experimental simulations also show the performance of theoretical results.

Highlights

We propose several succinct criteria to ensure global asymptotic stability and global asymptotic synchronization for a general class of memristive regulatory-type networks
Using memristive devices as synapses is a focus in memristive networks
To extract the benefits of high-efficiency memristive memory, various memristive networks have been reported to date [1–18]

Summary

Introduction

Using memristive devices as synapses is a focus in memristive networks. To extract the benefits of high-efficiency memristive memory, various memristive networks have been reported to date [1–18]. Compared with some memristive systems, a memristive regulatory-type network has the following advantages: (1) it is more biomimetic in behaviors with simple system structure; (2) it simplifies the structure and complication of circuits and is easy to realize. Advances in Mathematical Physics networks could be responsible for different neuromorphic architectures [36, 37] To this end, we focus on the evolution of memristive regulatory-type networks. Based on M-matrix theory, we develop less conservative global asymptotic stability results and global asymptotic synchronization results for memristive regulatory-type networks. Such theoretical analysis can significantly help understand and identify system performance, especially in neuromorphic computing era where stability or synchronization is crucial.

Model Description and Preliminaries

Main Results

Illustrative Examples

Conclusion