Spatiotemporal Dynamics of Mesoscopic Chaotic Systems
  An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide a mesoscopic description of the dynamics. The global and local dynamics is studied as a function of system size and diffusion coefficient. When the diffusion length is comparable to the system size phase coherence is maintained but the amplitudes of the oscillations are uncorrelated due to interaction between fluctuations and the instability of the chaotic dynamics. If the diffusion length is small compared to the system size then phase turbulence serves to destroy the noisy global attractor. 
Raymond Kapral, Xiao-Guang Wu