title: Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo.
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.
authors.affiliation: School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
authors.forename: Zhouchao
authors.identifier: 000000016981748X
authors.initials: Z
authors.lastname: Wei
authors.affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, England.
authors.forename: Irene
authors.initials: I
authors.lastname: Moroz
authors.affiliation: Department of Physics, University of Wisconsin - Madison, Madison, Wisconsin 53706, USA.
authors.forename: J C
authors.identifier: 0000000170143283
authors.initials: JC
authors.lastname: Sprott
authors.affiliation: Department of Electrical and Electronic Engineering, Faculty of Technology, Sakarya University, Sakarya 54050, Turkey.
authors.forename: Akif
authors.identifier: 0000000191513052
authors.initials: A
authors.lastname: Akgul
authors.affiliation: College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang