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Complex Modified Projective Synchronization for Fractional-order Chaotic Complex Systems

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Abstract

The aim of this paper is to study complex modified projective synchronization (CMPS) between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rössler system driving fractional-order complex Chen system, and fractional-order complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.

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Acknowledgements

This work was supported by Key Program of National Natural Science Foundation of China (No. 61533011) and National Natural Science Foundation of China (Nos. 61273088 and 61603203).

Author information

Authors and Affiliations

  1. College of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Cui-Mei Jiang & Shu-Tang Liu

  2. School of Electrical Engineering and Automation, Qilu University of Technology, Jinan, 250353, China

    Fang-Fang Zhang

Authors
  1. Cui-Mei Jiang
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  2. Shu-Tang Liu
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  3. Fang-Fang Zhang
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Corresponding author

Correspondence to Shu-Tang Liu.

Additional information

Recommended by Associate Editor Ivan Zelinka

Cui-Mei Jiang received the B. Sc. degree from Shandong Normal University, China in 2004. She received the M. Sc. degree from Ocean University of China, China in 2007. Then, she had worked for six years as a lecturer in Qingdao Technological University, China. She is currently a Ph. D. degree candidate at Shandong University, China.

Her research interests include adaptive control and chaos control.

Shu-Tang Liu received the Ph.D. degree in control theory and control engineering from South China University of Technology and City University of Hong Kong, China in 2002. From 2003 to 2005, he was doing postdoctoral research at Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China. Presently, he is a professor and doctoral supervisor at College of Control Science and Engineering, Shandong University, China.

His research interests include spatial chaotic theory of nonlinear dynamical systems and their applications, qualitative theory and qualitative control of complex systems, control and applications of fractals.

Fang-Fang Zhang received the B. Sc. degree from Northeast Petroleum University, China in 2003. She received the M. Sc. degree from Beijing University of Technology, China in 2006. She received the Ph.D. degree in control theory and control engineering from Shandong University, China in 2013. She is currently an associate professor of Qilu University of Technology, China.

Her research interests include adaptive control, chaos control and intelligent control.

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Jiang, CM., Liu, ST. & Zhang, FF. Complex Modified Projective Synchronization for Fractional-order Chaotic Complex Systems. Int. J. Autom. Comput. 15, 603–615 (2018). https://doi.org/10.1007/s11633-016-0985-3

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  • DOI: https://doi.org/10.1007/s11633-016-0985-3

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