Kresimir Josic, C. Eugene Wayne
Dynamics of a Ring of Diffusively Coupled Lorenz Oscillators
(5634K, postscript)

ABSTRACT.  We study the dynamics of a finite chain of 
diffusively coupled Lorenz oscillators with periodic boundary 
conditions. Such rings possess infinitely many fixed states, some of 
which are observed to be stable. It is shown that there exists a 
stable fixed state in arbitrarily large rings for a fixed coupling 
strength. This suggests that coherent behavior in networks of 
diffusively coupled systems may appear at a coupling strength 
that is independent of the size of the network.