Size dependence, coherence, and scaling in turbulent coupled-map lattices

In this paper the crossover from ‘‘small’’ to ‘‘large’’ chaotic systems is studied. The behavior of the largest Lyapunov exponent in a system of coupled chaotic maps shows that this crossover is remarkably sharp, and allows us to define a coherence length beyond which the system is effectively large. Between the coherent chaos of the small system and the incoherent chaos (turbulence) of the large one there is a stable window starting at the linear instability point for the uniform chaotic state in which the lattice becomes effectively one dimensional. The scaling of the coherence length close to the onset of turbulence is investigated and compared to recent predictions.