Analytical study of spatiotemporal chaos control by applying local injections

Spatiotemporal chaos control by applying local feedback injections is investigated analytically. The influence of gradient force on the controllability is investigated. It is shown that as the gradient force of the system is larger than a critical value, local control can reach very high efficiency to drive the turbulent system of infinite size to a regular target state by using a single control signal. The complex Ginzburg-Landau equation is used as a model to confirm the above analysis, and a four-wave-mixing mode is revealed to determine the dynamical behavior of the controlled system at the onset of instability.