Abstract

Spatiotemporal chaos (STC) refers to the state where a spatially extended system is chaotic in time and irregular in space. Several works have tried to identify the mechanisms for transition to STC . As one varies a control parameter (e.g., Reynolds number – Re), at some critical value the spatially homogeneous steady state becomes unstable with respect to small perturbations, giving rise to periodic oscillations. For increasing Re, other instabilities lead to symmetry breaking of spatiotemporal patterns, resulting in states that are disordered in space and time. There are several different routes to spatiotemporal chaos. This work focuses on crisis transitions to STC . As a control parameter is increased, the system undergoes a transition from quasiperiodicity to temporal chaos, then to spatiotemporal chaos, after a global bifurcation. The resulting time series displays on-off intermittency, characterized by random switching between laminar and bursty phases. Nonattracting chaotic sets known as chaotic saddles, present in a chaotic attractor, are shown to be responsible for these phases. Prior to the transition to STC , chaotic saddles are responsible for transient spatiotemporal chaos. The results are exemplified with two nonlinear partial differential equations with applications to fluids and plasmas: the Kuramoto-Sivashinsky and the regularized long-wave equations. Possible applications to nonlinear dynamo theory are discussed.