Regional Chaos Synchronization towards controlling high-dimensional open environmental systems
Abstract
Although controlling chaos can be regarded as a form of chaos synchronization, conventional chaos synchronization does not provide a practical framework for controlling high-dimensional open chaotic systems, such as weather. In high-dimensional open environmental systems, it is simply impossible to make the difference between drive and response systems asymptotically approach zero over the entire domain. Instead of conventional global chaos synchronization, here I define regional chaos synchronization, in which state variables within only a small target region are synchronized with a target trajectory using actuators located in the target region. Theoretical considerations and numerical experiments show that the performance of regional chaos synchronization is substantially degraded by the injection of errors from exterior regions that the controller is not intended to modify. Even under the same actuator specifications, the performances of regional chaos synchronization differ among trajectories, which is not the case of conventional global chaos synchronization. An appropriate target trajectory differs substantially from the natural trajectory only in the target region. This choice of target trajectories can minimize the injection of errors from exterior regions and thereby enable successful regional chaos synchronization. The implications of this new framework for realistic control problems such as weather control are discussed.