List of figures of 6 van der Pol Oscillators

These figures accompany the article ``Observing the symmetry of attractors,'' by Schenker and Swift. Physica D 114 (1998) pp. 315-337. If you don't have the paper, you may send Jim.Swift@nau.edu e-mail requesting a hard copy reprint.

The phase space of the 6 coupled oscillators is 12-dimensional. Click here for the equations. The figure shows two views of a 3-dimensional projection of the attractor into the space V1 + V0, which is a faithful representation space of D6 x Z2.

In all the figures, the top view is the representation space V1, and the bottom is a `side view' of V1 + V0. The symmetry group of the dynamical system is D6 x Z2. The dihedral group D6 acts on the top view in the usual way, and Z2 acts as inversion through the origin in both views.
Note that the bottom view is not a representation space of D6 x Z2, but it is a reprsentation space of Z2 x Z2, where the first Z2 is the 180 degree rotation in D6.

The parameter in the problem is gamma. You can choose a figure by clicking its icon, or by clicking the parameter value. You can also look at two figures at a time, showing the bifurcations.

               

gam = -2.2   gam = -2.3   gam = -2.4   gam = -2.5   gam = -4.2765   gam = -4.2766   gam = -4.5   gam = -4.6
gamma = -2.2 /-2.3     gamma = -2.4 /-2.5     gamma = -4.2765 /-4.2766     gamma = -4.5 /-4.6    
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