Conjecture on the dimensions of chaotic attractors of delayed-feedback dynamical systems

The Lyapunov dimension of chaotic attractors is found to be almost equal to the delay time divided by the correlation time of the feedback driving force for three dynamical systems: Mackey-Glass model for white-cell production, optical bistable hybrid system, and nonlinear ring cavity. This discovery will enable experimentalists to estimate the complexity of a high-dimension system much more easily than by time-series methods, as illustrated by a hybrid experiment.