Control of low-dimensional spatiotemporal chaos in Fourier space

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Abstract
A method is proposed whereby spatiotemporal chaos with few degrees of freedom is controlled via small and occasional feedback perturbations. The state of the system is monitored in Fourier space, using the fact that a few major modes may account for the essentials of the dynamics. Several unstable periodic orbits showing spatiotemporal structure are stabilized in the one-dimensional Kuramoto-Sivashinsky equation in the chaotic regime. This equation constitutes a link between dissipative systems displaying low-dimensional temporal chaos and the phase turbulence seen in a class of extended systems described by partial differential equations.

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