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Open AccessArticle

Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

by 1,2
1
School of Mathematical Sciences, University of Ji'nan, Ji'nan 250022, China
2
School of Control Science and Engineering, Shandong University, Ji'nan 250061, China
Entropy 2014, 16(12), 6195-6211; https://doi.org/10.3390/e16126195
Received: 27 August 2014 / Revised: 16 November 2014 / Accepted: 17 November 2014 / Published: 27 November 2014
(This article belongs to the Special Issue Complex Systems and Nonlinear Dynamics)
This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively. View Full-Text
Keywords: complex modified hybrid projective synchronization; chaos with complex variable; different dimension; fractional-order complex modified hybrid projective synchronization; chaos with complex variable; different dimension; fractional-order
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MDPI and ACS Style

Liu, J. Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos. Entropy 2014, 16, 6195-6211. https://doi.org/10.3390/e16126195

AMA Style

Liu J. Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos. Entropy. 2014; 16(12):6195-6211. https://doi.org/10.3390/e16126195

Chicago/Turabian Style

Liu, Jian. 2014. "Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos" Entropy 16, no. 12: 6195-6211. https://doi.org/10.3390/e16126195

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