Abstract
The study of low-dimensional dissipative dynamical systems has provided a reasonable understanding of the transition to temporal chaos in strongly confined systems for which the spatial structure can be considered as frozen. The situation is still less advanced for weakly confined systems where chaos has both a spatial and a temporal meaning. In order to approach the specificities of the latter, we have chosen to study first a partial differential equation (PDE) displaying a convective-type nonlinear term, steady cellular solutions as in convection, and a transition to spatiotemporal chaos, namely the damped Kuramoto-Sivashinsky (KS) equation: $${\partial _t}\phi + \eta \phi + {\partial _{{x^2}}}\phi + {\partial _{{x^4}}}\phi + 2\phi {\partial _x}\phi = 0.$$ (1)
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