title: Periodic synchronization control of discontinuous delayed networks by using extended Filippov-framework.
abstract: This paper is concerned with the periodic synchronization problem for a general class of delayed neural networks (DNNs) with discontinuous neuron activation. One of the purposes is to analyze the problem of periodic orbits. To do so, we introduce new tools including inequality techniques and Kakutani's fixed point theorem of set-valued maps to derive the existence of periodic solution. Another purpose is to design a switching state-feedback control for realizing global exponential synchronization of the drive-response network system with periodic coefficients. Unlike the previous works on periodic synchronization of neural network, both the neuron activations and controllers in this paper are allowed to be discontinuous. Moreover, owing to the occurrence of delays in neuron signal, the neural network model is described by the functional differential equation. So we introduce extended Filippov-framework to deal with the basic issues of solutions for discontinuous DNNs. Finally, two examples and simulation experiments are given to illustrate the proposed method and main results which have an important instructional significance in the design of periodic synchronized DNNs circuits involving discontinuous or switching factors.
authors.affiliation: Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, PR China. Electronic address: caizuowei01@126.com.
authors.forename: Zuowei
authors.initials: Z
authors.lastname: Cai
authors.affiliation: Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, PR China; College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China. Electronic address: lhhuang@hnu.edu.cn.
authors.forename: Lihong
authors.initials: L
authors.lastname: Huang
authors.affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China; Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong. Electronic address: zyguo@hnu.edu.cn.
authors.forename: Zhenyuan
authors.initials: Z
authors.lastname: Guo
authors.affiliation: Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, PR China.
authors.forename: Lingling
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, PR China.
authors.forename: Xuting
authors.initials: X
authors.lastname: Wan
mesh_terms: D000465:Algorithms; D005246:Feedback; D006801:Humans; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D013997:Time Factors
keywords: Discontinuous neuron activations; Filippov-framework; Functional differential inclusions; Neural networks; Periodic synchronization; Switching state-feedback control