Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems

Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Aug;92(2):022912. doi: 10.1103/PhysRevE.92.022912. Epub 2015 Aug 19.

Abstract

We present an alternative 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 or 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.