Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems

Gomes, S. N.; Pradas, M.; Kalliadasis, S.; Papageorgiou, D. T. and Pavliotis, G. A. (2015). Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems. Physical Review E, 92(2), article no. 022912.

DOI: https://doi.org/10.1103/PhysRevE.92.022912

Abstract

We present a new methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones/bound states) and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures.

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