Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters

This paper focuses on the adaptivemodified hybrid function projective synchronization with complex function transformationmatrix (CMHFPS) for different dimensional chaotic (hyperchaotic) systemswith 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 squarematrix, 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 preJ. Liu (B) School of Mathematical Sciences, University of Ji’nan, Jinan 250022, Shandong, People’s Rupublic of China e-mail: [email protected] S. Liu School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, People’s Rupublic of China e-mail: [email protected] J. C. Sprott Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA e-mail: [email protected] sented to illustrate the effectiveness and feasibility of the theoretical results.