Adaptive Complex Modified Hybrid Function Projective Synchronization of Different Dimensional Complex Chaos with Uncertain Complex Parameters

Jian Liu
School of Mathematical Sciences,
University of Ji'nan, Jinan 250022,
Shandong, People's Republic of China

Shutang Liu
School of Control Science and Engineering,
Shandong University, Jinan 250061
Shandong, People's Republic of China

J. C. Sprott
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA

Received: 14 February 2015 / Accepted: 5 September 2015 / Published online: 15 September 2015


This paper focuses on the adaptive modified hybrid function projective synchronization with complex function transformation matrix (CMHFPS) for different dimensional chaotic (hyperchaotic) systems with complex variables and unknown complex parameters. The chaotic systems are considerably different from those in the existing closely related literature. Moreover, the transformation matrix in this type of chaos synchronization is not a square matrix, and its elements are complex functions, In particular, by constructing appropriate Lyapunov functions dependent on complex variables, the adaptive controllers are designed to synchronize different dimensional complex chaos (hyperchaos) with complex parameters in the sense of CMHFPS, and the complex update laws for estimating unknown complex parameters of complex chaotic systems are also given. Finally, two examples are presented to illustrate the effectiveness and feasibility of the theoretical results.

Ref: J. Liu, S. Liu, and  J. C. Sprott, Nonlinear Dynamics 83, 1109-1121 (2016)

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