IEICE Electronics Express
Online ISSN : 1349-2543
LETTER
A novel four-wing strange attractor born in bistability
Chunbiao LiIhsan PehlivanJulien Clinton SprottAkif Akgul
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2015 Volume 12 Issue 4 Pages 20141116

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Abstract

Attractor merging can exist in chaotic systems with some kind of symmetry, which makes it possible to form a four-wing attractor from a bistable system. A relatively simple such case is described, which has robust chaos varying from a pair of coexisting symmetric single-wing attractors to a double-wing butterfly attractor, and finally to a four-wing attractor. Basic dynamical characteristics of the system are demonstrated in terms of equilibria, Jacobian matrices, Lyapunov exponents, and Poincaré sections. From a broad exploration of the dynamical regions, we observe robust chaos with embedded Arnold tongues of periodicity in selected parameter regions. The chaotic system with a wing structure has four nonlinear quadratic terms, one of the coefficients of which is a hidden isolated amplitude parameter, by which one can control the amplitude of two of the variables. The corresponding chaotic circuit with an amplitude-control knob is designed and implemented, which generates a four-wing attractor with adjustable amplitude.

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© 2015 by The Institute of Electronics, Information and Communication Engineers
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