A Novel Four-wing Strange Attractor Born in Bistability

Chunbiao Li¹, Ihsan Pehlivan², Julien Clinton Sprott³, and Akif Akgul²

¹School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

²Department of Electric and Electronic Engineering, University of Sakarya, Sakarya, Turkey

³Department of Physics, University of Wisconsin - Madison, Madison, USA

(Received November 27, 2014, Accepted January 20, 2015, Publicized February 3, 2015, Copyedited February 25, 2015)

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.

Ref: C. Li, I. Pehlivan, J. C. Sprott, and A. Akgul, IEICE Electronics Express 12, 1-12 (2015)

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