sprott@physics.wisc.edu

Received August 9, 2013

ABSTRACT

A chaotic flow has an involutional
symmetry if the form of the dynamical equations remains
unchanged when one or more of the variables changes sign. Such
systems are of theoretical and practical importance because they
can exhibit symmetry breaking in which a symmetric pair of
attractors coexist and merge into one symmetric attractor
through an attractor-merging bifurcation. This paper describes
the simplest chaotic examples of such systems in three
dimensions, including several cases not previously known, and
illustrates the attractor-merging process.

Ref: J. C. Sprott, International
Journal of Bifurcation and Chaos 24,
1450009 (2014)

The complete paper is available in
PDF format.

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Fig. 1. Moore-Spiegel attractor from Eq. (1) with

Fig. 2. Attractor merging from Eq. (2) with

Fig. 3. Coexisting Malasoma strange attractors with

Fig. 4. Coexisting strange attractors in the Lorenz system with

Fig. 5. Attractor merging for Eq. (5).

Fig. 6. Cross-section of the fractal basins of attraction in the

Fig. 7. Attractor merging for Eq. (6) with

Fig. 8. Attractor "kissing" for Eq. (8).