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Control schemes for dynamical systems typically involve stabilizing unstableperiodic orbits. In this paper we introduce a new paradigm of control thatinvolves `trapping' the dynamics arbitrarily close to any desired trajectory.This is achieved by a state-dependent dynamical selection of the input signalapplied to the driven nonlinear system. An emergent property of the trappingprocess is that the signal changes in a chaotic sequence: a manifestation ofchaos-induced order. The simplicity of the control scheme makes it easilyimplementable in experimental systems.

Designer dynamics through chaotic traps: Controlling complex behavior in driven nonlinear systems