Controlling spatiotemporal chaos in coupled map lattice systems

A spatiotemporal system is modeled by a coupled map lattice. Feedback pinnings are used to control chaos of the system by stabilizing a certain unstable reference state. As the pinning distribution is dense enough, the unstable state can be stabilized. If the density is low, the reference state may not be approached asymptotically. In this case, however, the pinnings can still effectively suppress chaos and produce rich spatiotemporal structures. If a solution is locally stable while the transient process to this state is extremely long and chaotic, pinnings of very low density can well control the transient chaos.