Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo

Zhouchao Wei,^1,2,3,4,a) Irene Moroz,³ J. C. Sprott,⁵ Akif Akgul,⁶ and Wei Zhang⁴

¹School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
²Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data
Processing, Yulin Normal University, Yulin 537000, China
³Mathematical Institute, University of Oxford, Oxford OX2 6GG, England
⁴College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
⁵Department of Physics, University of Wisconsin - Madison, Madison, Wisconsin 53706, USA
⁶Department of Electrical and Electronic Engineering, Faculty of Technology, Sakarya University,
Sakarya 54050, Turkey

(Received 21 December 2016; accepted 13 February 2017; published online 27 February 2017)

ABSTRACT

We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two stable equilibrium states in certain regions of parameter space. The new 5D hyperchaotic self-exciting homopolar disc dynamo has multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, hidden chaos or hyperchaos, as well as coexisting attractors. We use numerical integrations to create the phase plane trajectories, produce bifurcation diagram, and compute Lyapunov exponents to verify the hidden attractors. Because no unstable equilibria exist in two parameter regions, the system has a multistability and six kinds of complex dynamic behaviors. To the best of our knowledge, this feature has not been previously reported in any other high-dimensional system. Moreover, the 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations. Both Matlab and the oscilloscope outputs produce similar phase portraits. Such implementations in real time represent
a new type of hidden attractor with important consequences for engineering applications.

Ref: Z. Wei, I. Moroz, J. C. Sprott, A. Akgul, and W. Zhang, Chaos 27, 033101-1 -- 033101-7 (2017)

The complete paper is available in PDF format.

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