Unidirectionally coupled map lattice as a model for open flow systems

Spatial development of turbulence is studied with the unidirectionally coupled logistic lattice model. The transition from absolute to convective instability is described. A numerical method allowing one to compute convectively unstable states without numerical artifacts is introduced and used to construct the phase diagram. The influence of external noise on the convectively unstable regimes is investigated numerically. Different types of noise-sustained structures are described. Statistical properties of frozen periodic patterns are derived analytically and compared with the numerical results. {} 1996 The American Physical Society.