Controllability of spatiotemporal systems using constant pinnings

Abstract

Most natural spatiotemporal systems are an organized ensemble of dynamical subsystems whose behaviour is regulated by nonlinearly coupled multi-variable processes. The response of each of these variables and/or combinations of them to any single or composite external perturbation can influence its spatiotemporal behaviour in a complex and non-intuitive manner. This paper attempts to study the dynamical response of two coupled map lattice systems having local dynamics described by (a) coupled discrete maps, and (b) coupled differential equations, to external perturbation (or "pinning") applied to each variable individually or simultaneously. We show that the response of different variables to external pinning is quite different. Our results indicate that, though this pinning approach is useful in controlling complex dynamics both globally and locally, enhancing complexity in dynamics ("anti-control") is variable dependent. Thus complete controllability (i.e., control and anti-control) of dynamics in these spatially extended systems having coupled multi-variable processes does not only depend on the sign and strength of the perturbation, but also on the specific variable being pinned. This also implies that external manipulation of state variables in natural systems can lead to quite different responses depending at the level of action of the perturbation.