New results of exponential synchronization of complex network with time-varying delays

• Published in: Advances in difference equations Vol. 2019; no. 1; pp. 1 - 18
• Main Authors: Luo, Yiping, Ling, Zhaoming, Cheng, Zifeng, Zhou, Bifeng
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 14.01.2019; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Complex network; Computer simulation; Control stability; Controllers; Damping; Delay; Difference and Functional Equations; Exponential synchronization; Feedback control; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Razumikhin theorem; Synchronism; Time synchronization; Time-varying delay; Exponential synchronization; Time-varying delay; Complex network; Razumikhin theorem
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-019-1947-1

In this study, we elucidated the exponential synchronization of a complex network system with time-varying delay. Then the exponential synchronization control of several types of complex network systems with time-varying delay under no requirements of delay derivable were explored. The dynamic behavior of a system node shows time-varying delays. Thus, to derive suitable conditions for the exponential synchronization of different complex network systems, we designed a linear feedback controller for linear coupling functions, using the Lyapunov stability theory, Razumikhin theorem, and Newton–Leibniz formula. The exponential damping rates for the exponential synchronization of different complex network systems were then estimated. Finally, we validated our conclusions through a numerical simulation.