CONTROLLING THE DYNAMICAL BEHAVIOR OF A CIRCLE MAP MODEL OF THE HUMANHEART

One-dimensional circle maps are good models for describing the nonline ar dynamical behavior of two interacting oscillators. They have been e mployed to characterize the interaction between a periodic external fo rcing stimulus and an in vitro preparation of chick embryonic cardiac cells. They have also been used to model some human cardiac arrythmias such as modulated ventricular parasystole. In this paper, we describe several techniques involving engineering feedback control theory appl ied to a circle map model of human heart parasystole. Through simulati ons of the mathematical model, we demonstrate that a desired target ph ase relationship between the normal sinus rhythm and an abnormal ectop ic pacemaker can be achieved rapidly with low-level external stimulati on applied to the system. Specifically, we elucidate the linear, self- tuning, and nonlinear feedback approaches to control. The nonlinear me thods are the fastest and most accurate, yet the most complex and comp utationally expensive to implement of the three types. The linear appr oach is the easiest to implement but may not be accurate enough in rea l applications, and the self-tuning methods are a compromise between t he other two. The latter was successful in tracking a variety of perio d-1, period-2, and period-3 target phase trajectories of the heart mod el.