Spatial development of chaos in nonlinear media

Abstract

Spatial development of chaos in the media, where initial disturbances are advected (flow systems, systems with convective character of wave instability) is investigated. The problem is formulated as the study of nonlinear transformation of external perturbations, prescribed at a boundary. It is shown that the periodic field remains periodic but may be unstable with respect to secondary perturbations. Transformation of a quasiperiodic field leads to oscillations with a dense spectrum, practically undistinguishable from chaotic oscillations. In a model, where with change of a parameter convective instability turns into absolute instability, a regime of spatially period-doubling waves is found.