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Author:

Wei, Zhouchao (Wei, Zhouchao.) | Moroz, Irene (Moroz, Irene.) | Sprott, J. C. (Sprott, J. C..) | Akgul, Akif (Akgul, Akif.) | Zhang, Wei (Zhang, Wei.)

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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. Published by AIP Publishing.

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Author Community:

  • [ 1 ] [Wei, Zhouchao]China Univ Geosciences, Sch Math & Phys, Wuhan 430074, Peoples R China
  • [ 2 ] [Wei, Zhouchao]Yulin Normal Univ, Guangxi Coll, Univ Key Lab Complex Syst Optimizat & Big Data Pr, Yulin 537000, Peoples R China
  • [ 3 ] [Wei, Zhouchao]Univ Oxford, Math Inst, Oxford OX2 6GG, England
  • [ 4 ] [Moroz, Irene]Univ Oxford, Math Inst, Oxford OX2 6GG, England
  • [ 5 ] [Wei, Zhouchao]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 6 ] [Zhang, Wei]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 7 ] [Sprott, J. C.]Univ Wisconsin, Dept Phys, Madison, WI 53706 USA
  • [ 8 ] [Akgul, Akif]Sakarya Univ, Fac Technol, Dept Elect & Elect Engn, TR-54050 Sakarya, Turkey

Reprint Author's Address:

  • [Wei, Zhouchao]China Univ Geosciences, Sch Math & Phys, Wuhan 430074, Peoples R China;;[Wei, Zhouchao]Yulin Normal Univ, Guangxi Coll, Univ Key Lab Complex Syst Optimizat & Big Data Pr, Yulin 537000, Peoples R China;;[Wei, Zhouchao]Univ Oxford, Math Inst, Oxford OX2 6GG, England;;[Wei, Zhouchao]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

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Source :

CHAOS

ISSN: 1054-1500

Year: 2017

Issue: 3

Volume: 27

2 . 9 0 0

JCR@2022

ESI Discipline: PHYSICS;

ESI HC Threshold:158

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 155

SCOPUS Cited Count: 154

ESI Highly Cited Papers on the List: 22 Unfold All

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WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 11

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