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Volume 2017 (2017), Article ID 7101927, 11 pages
Research Article

Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria

1Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China
2School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
3Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
4Department of Computer Technologies, Vocational School of Karacabey, Uludağ University, Karacabey, 16700 Bursa, Turkey
5Department of Electrical and Electronic Engineering, Faculty of Technology, Sakarya University, Adapazarı, Turkey

Correspondence should be addressed to Zhouchao Wei

Received 3 February 2017; Accepted 19 March 2017; Published 31 May 2017

Academic Editor: Karthikeyan Rajagopal

Copyright © 2017 Yu Feng 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.


We introduce and investigate a four-dimensional hidden hyperchaotic system without equilibria, which is obtained by augmenting the three-dimensional self-exciting homopolar disc dynamo due to Moffatt with an additional control variable. Synchronization of two such coupled disc dynamo models is investigated by active control and sliding mode control methods. Numerical integrations show that sliding mode control provides a better synchronization in time but causes chattering. The solution is obtained by switching to active control when the synchronization errors become very small. In addition, the electronic circuit of the four-dimensional hyperchaotic system has been realized in ORCAD-PSpice and on the oscilloscope by amplitude values, verifying the results from the numerical experiments.