Reaction-diffusion system with Brusselator kinetics: Control of a quasiperiodic route to chaos

A methodology for controlling complex dynamics and chaos in distributed parameter systems is discussed. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling route to chaos exists in a defined range of parameter values, is used as an example. Poincar\'e maps and singular value decomposition are used for characterization of quasiperiodic and chaotic attractors and for the identification of dominant modes. Tested modal feedback control schemes based on identified dominant spatial modes confirm the possibility of stabilization of simple quasiperiodic trajectories in the complex quasiperiodic or chaotic spatiotemporal patterns.