Coexisting Hidden Attractors in a 4-D Simplified Lorenz System

Chunbiao Li
School of Information Science and Engineering
Southeast University, Nanjing 210096, P. R. China
Engineering Technology Research and Development
Center of Jiangsu Circulation Modernization Sensor Network
Jiangsu Institute of Commerce, Nanjing 210007, P. R. China
Department of Physics, University of Wisconsin-Madison,

Madison, WI 53706, USA

J. C. Sprott
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA

Received September 6, 2013

ABSTRACT

A new simple four-dimensional equilibrium-free autonomous ODE system is described. The system has seven terms, two quadratic nonlinearities, and only two parameters. Its Jacobian matrix everywhere has rank less than 4. It is hyperchaotic in some regions of parameter space, while in other regions it has an attracting torus that coexists with either a symmetric pair of strange attractors or with a symmetric pair of limit cycles whose basin boundaries have an intricate fractal structure. In other regions of parameter space, it has three coexisting limit cycles and Arnold tongues. Since there are no equilibria, all the attractors are hidden. This combination of features has not been previously reported in any other system, especially one as simple as this.

Ref: C. Li and  J. C. Sprott, International Journal of Bifurcation and Chaos 24, 1450034 (2014)

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