Entropy 2014, 16(12), 6195-6211; doi:10.3390/e16126195
Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos
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
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)
Abstract
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-TextKeywords:
complex modified hybrid projective synchronization; chaos with complex variable; different dimension; fractional-order
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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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.