Multistability in the Lorenz System: A Broken Butterfly
Chunbiao Li
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
Julien Clinton Sprott
Department of Physics, University of Wisconsin--Madison,
Madison, WI 53706, USA
Received: April 30, 2014
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.