Multistability in the Lorenz System: A Broken Butterfly

作者:Li, Chunbiao*; Sprott, Julien Clinton
来源:International Journal of Bifurcation and Chaos, 2014, 24(10): 1450131.
DOI:10.1142/S0218127414501314

摘要

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.