Feedback control of a quadratic map model of cardiac chaos

This paper describes methods based on engineering feedback principles for controlling cardiac chaos modeled by a quadratic map. We first discuss briefly the linear approach which is effective at controlling the map to fixed point or near fixed point target trajectories. We then describe and demonstrate self-tuning methods that can control the chaotic orbits of the map to arbitrary period one, two, or three target trajectories. We conclude with a discussion comparing the merits of this approach to the OGY method used by Garfinkel et al. [1992] for control of complex rhythms in rabbit septal preparations, and to the hat-topped quadratic mapping method of Glass and Zeng [1994].