Control of chaos by capture and release

We propose and demonstrate a different method for the control of flip saddles in dissipative chaotic systems. Due to the dynamics of a flip saddle, the stable manifolds of a target orbit and its perturbation can be modeled as a pair of concentric Möbius bands. Over the period of the target orbit, these bands rotate relative to one another. The method of capture and release (CR) takes advantage of this rotation, and captures a nearby system state in the perturbed stable manifold, releasing it when the rotation of the Möbius bands brings them into alignment. Unlike the method of Ott, Grebogi, and Yorke and most of its variants, CR does not rely on the unstable component of the flow to push the system state onto the stable manifold; the system state is evolving in a stable subspace for the duration of the control perturbation.