Periodicity and finite-time periodic synchronization of discontinuous complex-valued neural networks

Zengyun Wang; Jinde Cao; Zuowei Cai; Lihong Huang

doi:10.1016/j.neunet.2019.08.021

Periodicity and finite-time periodic synchronization of discontinuous complex-valued neural networks

Neural Netw. 2019 Nov:119:249-260. doi: 10.1016/j.neunet.2019.08.021. Epub 2019 Aug 26.

Authors

Zengyun Wang¹, Jinde Cao², Zuowei Cai³, Lihong Huang⁴

Affiliations

¹ Department of Mathematics, Hunan First Normal University, Changsha 410205, China; School of Mathematics, Southeast University, Nanjing, 210096, China; The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, Southeast University, Nanjing 210096, China; Changsha University of Science and Technology, Changsha, 410114, China.
² School of Mathematics, Southeast University, Nanjing, 210096, China; The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, Southeast University, Nanjing 210096, China. Electronic address: jdcao@seu.edu.cn.
³ Department of Technology, Hunan Women's University, Changsha, Hunan 410002, China; Changsha University of Science and Technology, Changsha, 410114, China. Electronic address: caizuowei01@126.com.
⁴ Changsha University of Science and Technology, Changsha, 410114, China.

PMID: 31472291
DOI: 10.1016/j.neunet.2019.08.021

Abstract

This paper discusses the issue of periodicity and finite-time periodic synchronization of discontinuous complex-valued neural networks (CVNNs). Based on a modified version of Kakutani's fixed point theorem, general conditions are obtained to guarantee the periodicity of discontinuous CVNNs. Next, several criteria for finite-time periodic synchronization (FTPS) are given by using a new proposed finite-time convergence theorem. Different from the traditional convergence lemma, the estimated upper bound of the derivative of the Lyapunov function (LF) is allowed to be indefinite or even positive. In order to achieve FTPS, novel discontinuous control algorithms, including state-feedback control algorithm and generalized pinning control algorithm, are designed. In the generalized pinning control algorithm, a guideline is proposed to select neurons to pin the designed controller. Finally, two simulations are given to substantiate the main results.

Keywords: Differential inclusion; Discontinuous complex-valued neural networks; Finite-time periodic synchronization; Kakutans fixed point theorem; Periodic solution.

MeSH terms

Algorithms
Feedback
Neural Networks, Computer*
Neurons / physiology*
Periodicity*
Time Factors