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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 257327, 16 pages
http://dx.doi.org/10.1155/2014/257327
Research Article

A Novel Four-Wing Hyperchaotic Complex System and Its Complex Modified Hybrid Projective Synchronization with Different Dimensions

1School of Control Science and Engineering, Shandong University, Ji’nan 250061, China
2School of Mathematical Sciences, University of Ji’nan, Ji’nan 250022, China

Received 4 March 2014; Revised 12 May 2014; Accepted 16 May 2014; Published 5 June 2014

Academic Editor: Shurong Sun

Copyright © 2014 Jian Liu et al. 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.

Abstract

We introduce a new Dadras system with complex variables which can exhibit both four-wing hyperchaotic and chaotic attractors. Some dynamic properties of the system have been described including Lyapunov exponents, fractal dimensions, and Poincaré maps. More importantly, we focus on a new type of synchronization method of modified hybrid project synchronization with complex transformation matrix (CMHPS) for different dimensional hyperchaotic and chaotic complex systems with complex parameters, where the drive and response systems can be asymptotically synchronized up to a desired complex transformation matrix, not a diagonal matrix. Furthermore, CMHPS between the novel hyperchaotic Dadras complex system and other two different dimensional complex chaotic systems is provided as an example to discuss increased order synchronization and reduced order synchronization, respectively. Numerical results verify the feasibility and effectiveness of the presented schemes.