Localized Control of Spatiotemporal Chaos

Many physical, chemical, and biological systems of interest evolve in a nonequilibrium environment. As these systems are driven further out of equilibrium, they tend to display progressively more complicated dynamics, with steady spatially uniform states replaced first by non-chaotic patterned states and eventually by spatiotemporal chaos. This complexity is often undesirable and considerable benefits could be derived by forcing the system towards a less complex (but usually unstable) steady or time-periodic state. In response to this challenge, control of spatiotemporal chaos has emerged in recent years as a problem of increasing fundamental and applied value. Control of turbulent boundary flows [17], mechanical vibrations, and noise [37] is already an indispensable component of industrial design. Many other significant technological applications, such as mixing [62], optical fiber manufacture [70], coating [4, 39], wide aperture semiconductor lasers [56], inertial confinement [67], combustion [81], and chemical reactions [10], could crucially benefit from our ability to control (either suppress or enhance) the instabilities leading to complex spatiotemporal dynamics. Considerable effort is currently being invested in control of ventricular fibrillation [79] and epilepsy [23]. Besides these practical applications, the ability to control spatiotemporal dynamics opens up a whole new direction in fundamental research by providing a unique capability to study otherwise inaccessible unstable states of extended non-equilibrium systems. This capability can be used, for instance, to experimentally construct complete bifurcation diagrams [49], study the dynamics and stability of isolated modes [22], detect and study unstable recurrent patterns [5], or reproducibly impose initial conditions [74]. Although the first attempts to control spatiotemporally complex dynamics are centuries old, a scientific approach has not been employed until 1904, when boundary layer theory was developed by Prandtl [68]. Subsequent at-