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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 2313768, 13 pages
Research Article

Characteristic Analysis of Fractional-Order 4D Hyperchaotic Memristive Circuit

1School of Physics and Electronics, Central South University, Changsha 410083, China
2School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China

Correspondence should be addressed to Kehui Sun

Received 6 March 2017; Accepted 28 May 2017; Published 10 July 2017

Academic Editor: Alessandro Lo Schiavo

Copyright © 2017 Jun Mou 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.


Dynamical behaviors of the 4D hyperchaotic memristive circuit are analyzed with the system parameter. Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical solution of fractional-order 4D hyperchaotic memristive circuit is investigated. The distribution of stable and unstable regions of the fractional-order 4D hyperchaotic memristive circuit is determined, and dynamical characteristics are studied by phase portraits, Lyapunov exponents spectrum, and bifurcation diagram. Complexities are calculated by employing the spectral entropy (SE) algorithm and C0 algorithm. Complexity results are consistent with that of the bifurcation diagrams, and this means that complexity can also reflect the dynamic characteristics of a chaotic system. Results of this paper provide a theoretical and experimental basis for the application of fractional-order 4D hyperchaotic memristive circuit in the field of encryption and secure communication.