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Multistability in the Lorenz System: A Broken Butterfly

School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, 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

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and

Julien Clinton Sprott

Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA

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https://doi.org/10.1142/S0218127414501314Cited by:172 (Source: Crossref)

Abstract

In this paper, the dynamical behavior of the Lorenz system is examined in a previously unexplored region of parameter space, in particular, where r is zero and b is negative. For certain values of the parameters, the classic butterfly attractor is broken into a symmetric pair of strange attractors, or it shrinks into a small attractor basin intermingled with the basins of a symmetric pair of limit cycles, which means that the system is bistable or tristable under certain conditions. Although the resulting system is no longer a plausible model of fluid convection, it may have application to other physical systems.

Keywords:

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