Correlation of entropy with optimal pinning density for the control of spatiotemporal chaos

We consider three systems that are spatially one-dimensional and are discretized in space and time: i) cellular automata proposed by Wolfram; ii) a system that has been used as a prototype for coupled map lattices; and iii) a coupled map lattice that provides a simple description of earthquakes. Chaotic modes of these systems can be made periodic by external forcing at points equidistant in space (”pinnings”). The minimum distance between these points corresponding to the optimal pinning density is correlated to the spatial measure entropy S via a single-valued relationship. In other words, determination of S straightforwardly yields optimal spacings for a forcing that turns unpredictable into predictable behaviour.