MULLTISTABILITY IN A BUTTERFLY FLOW

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 Economic and Trade Technology,
Nanjing 210007, P. R. China
Department of Physics, University of Wisconsin-Madison,

Madison, WI 53706-1390, USA

J. C. SPROTT
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706-1390, USA

Received June 5, 2013

ABSTRACT
A dynamical system with four quadratic nonlinearities is found to display a butterfly strange attractor. In a relatively large region of parameter space the system has coexisting point attractors and limit cycles. At some special parameter combinations, there are five coexisting attractors, where a limit cycle coexists with two equiilibrium points and two strange attractors in different attractor basins. The basin boundaries have a symmetric fractal structure. In addition, the system has other multistable regimes where a pair of point attractors coexist with a single limit cycle or a symmetric pair of limit cycles and where a symmetric pair of limit cycles coexist without any stable equilibria.

Ref: C. Li and  J. C. Sprott, International Journal of Bifurcation and Chaos 23, 1350199 (2013)

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