Modified function projective synchronization of complex dynamical networks with mixed time-varying and asymmetric coupling delays via new hybrid pinning adaptive control

Advances in Difference Equations

Piyapong Niamsup¹  Thongchai Botmart²  Wajaree Weera³ 

[1] Department of Mathematics, Chiang Mai University, Chiang Mai, Thailand;Department of Mathematics, Khon Kaen University, Khon Kaen, Thailand;Department of Mathematics, University of Pha Yao, Pha Yao, Thailand

关键词: modified function projective synchronization;    complex dynamical network;    mixed time-varying delay;    mixed coupling delays;    hybrid adaptive pinning control;   

DOI  :  10.1186/s13662-017-1183-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper investigates modified function projective synchronization (MFPS) for complex dynamical networks with mixed time-varying and hybrid asymmetric coupling delays, which is composed of state coupling, time-varying delay coupling and distributed time-varying delay coupling. In contrast to previous results, the coupling configuration matrix needs not be symmetric or irreducible. The MFPS of delayed complex dynamical networks is considered via either hybrid control or hybrid pinning control with nonlinear and adaptive linear feedback control, which contains error linear term, time-varying delay error linear term and distributed time-varying delay error linear term. Based on Lyapunov stability theory, adaptive control technique, the parameter update law and the technique of dealing with some integral terms, we will show that control may be used to manipulate the scaling functions matrix such that the drive system and response networks could be synchronized up to the desired scaling function matrix. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results in this article generalize and improve the corresponding results of the recent works.

【 授权许可】

CC BY