The entrainment and migration controls of multiple-attractor systems

A method of imposing limited controls on systems which can generally have complex dynamics with many dynamic attractors, is illustrated using several map-dynamics and the Lorenz system. The two types of controls involve: (a) the entrainment of the system, x, to a class of “entrainment goals” g(t), meaning that limt→∞ |x-g| = 0, and (b) the transfer of the system from one attractor to another, using “migration-goals” in the control.