These are equations (31) in our paper (p. 328 in reprint, p. 16 in preprint). 
xj' =  yj - delta(yj-1 + yj+1)
yj' = -xj + delta(xj-1 + xj+1)
      + yj(alpha - xj2) + beta(yj-1 + yj+1) + gamma(yj-2 + yj+2)
where the subscript j is defined modulo N. The parameter alpha determines the strength of the nonlinearity, and beta, gamma, and delta are coupling coefficients.
For section 3.3 of the paper, the parameters are 
N = 6 oscillators.
alpha = 1 (a moderate amount of nonlinearity.)
beta = 0.
gamma between -2 and -5.
delta = -0.1 (nonzero delta seemed to be necessary for chaotic behavior.)
Table 2, on p. 335/p. 24 of our paper shows the different types of symmetry and dynamics we observed. All of these types are shown here in the figures.

[Back] List of figures     [Back] Jim Swift's home page     [Back] Department of Mathematics     [Back] NAU Home Page