In this paper we study an iterated map that describes action potential durations (acronym: APD) in a single cardiac cell. In particular, we are interested in alternans, a term which refers to phase locked period-two APDs. Under certain parameter values, alternans are theoretically possible but are unstable and therefore not seen under normal pacing conditions. We would like to stabilize alternans under these conditions using feedback. In essence, a feedback scheme uses information about previous iterates of an iterated map function to perturb future iterates in order to force stability. This paper builds on previous work on feeback control, but in the somewhat different context here, a new feedback scheme must be constructed.
David Schaeffer, Department of Mathematics, Duke Universitydgs@math.duke.edu
Fischer, Matthew and Middleton, Colin
"Stabilizing a Subcritical Bifurcation in a Mapping Model of Cardiac-Membrane Dynamics,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7
, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/13