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.