Controlling chaos in systems described by partial differential equations

Abstract

A model one-dimensional drift-wave equation driven by a sinusoidal wave is used to study controlling chaos in partial differential equations. By injecting negative feedback through a monochromatic wave or pinning at a certain x-space point we can successfully stabilize unstable steady states and control chaos. In the case of bistability, an unstable steady state in the middle branch can be also stabilized by these controlling approaches. The methods used in this Letter can be applied to general continuous spatiotemporal systems.