3D Printing -- The Basins of Tristability in the Lorenz System


Anda Xiong and Julien C. Sprott
Physics Department, University of Wisconsin-Madison,
1150 University Avenue, Madison,
Wisconsin 53706, USA

Jingxuan Lyu and Xilu Wang
Mechanical Engineering Department,
University of Wisconsin-Madison,
1415 Engineering Drive, Madison,
Wisconsin 53706, USA

Received April 9, 2017

ABSTRACT

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tristable
system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

Ref: A. Xiong, J. C. Sprott, J. Lyu, and X. Wang, International Journal of Bifurcation and Chaos 27, 1750128 (2017)

The complete paper is available in PDF format.

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