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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Synchronization and Anti-synchronization for a 4-dimensional Hyperchaotic System

Journal of Vibration Testing and System Dynamics 4(4) (2020) 325--336 | DOI:10.5890/JVTSD.2020.12.003

Yuansheng Wang , Bo Li, Guiying Lu

School of Mechanics and Electrical Information, China University of Geoscience Wuhan, Hubei, 430074, China

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Between two 4-dimensional hyper-chaotic systems with unknown parameters, using Lyapunov stability theory, adaptive controller and parameter estimation law are designed to achieve their globally asymptotical synchronization and anti-synchronization. By numerical calculation with MATLAB, synchronization or anti-synchronization is arrived theoretically but synchronous or anti-synchronous errors of state variables cannot all converge to zero simultaneously during a limited time. The comparative and contrastive studies about system without cubic term indicates that the primary cause is existence of cubic term. It is verified by numerical simulation examples consistently.


This research is financially supported by the national major scientific instruments special fund (41827808).


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