This is a snapshot in time of the relative phases in an array of 400x400 nearest neighbor phase oscillators in a regime where synchrony is asymptotically stable. Initial conditions are a "spiral wave" which accounts for the symmetry of the pattern. The equations are of the form:

$$\frac{d x_j}{dt} = 1 + \sum_k H(x_k-x_j)$$

where the sum is over the 4 nearest neighbors. Boundary conditions are "natural" - the oscillators at the corneres or edges couple to 2 or 3 others.

$$
H(u) = a_1 \sin(u) + a_2 \sin(2u) + a_3 \sin(3u) + b_1 (1-\cos(u))+b_2(1-\cos(2u))+b_3 (1-\cos(3u))
$$

The plot shows \(y_j = x_j -x_0\) (subtracting upper left phase)

(Picture from a SIADS poster)

Author Institutional Affiliation | University of Pittsburg |

Author Email | |

Notes | Submitted by the Picture Gallery editors, not the original authors. |

Keywords | Applications SIADS |