Eur. Phys. J. B (2016) 89: 204
https://doi.org/10.1140/epjb/e2016-70337-6

Regular Article

Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network

¹ School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China
² School of Science, Shandong University of Technology, Zibo 255000, P.R. China
³ Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China

^a e-mail: lilixiang2006@163.com

Received: 26 May 2016
Received in final form: 2 July 2016
Published online: 21 September 2016

Abstract

In this paper, we study the finite-time stability and synchronization problem of a class of memristor-based fractional-order Cohen-Grossberg neural network (MFCGNN) with the fractional order α ∈ (0,1 ]. We utilize the set-valued map and Filippov differential inclusion to treat MFCGNN because it has discontinuous right-hand sides. By using the definition of Caputo fractional-order derivative, the definitions of finite-time stability and synchronization, Gronwall’s inequality and linear feedback controller, two new sufficient conditions are derived to ensure the finite-time stability of our proposed MFCGNN and achieve the finite-time synchronization of drive-response systems which are constituted by MFCGNNs. Finally, two numerical simulations are presented to verify the rightness of our proposed theorems.