Stabilizing a Subcritical Bifurcation in a Mapping Model of Cardiac-Membrane Dynamics

Authors

Matthew Fischer, Duke UniversityFollow
Colin Middleton, Duke University

Abstract

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.

Author Bio

Matthew Fischer graduated from Duke University in May 2006. He majored in Mathematics and Biology. He will be working for Cigna Healthcare in Hartford, CT following graduation.

Colin Middleton graduated from Duke University in May 2005 where he majored in Mathematics. Colin has been working as a High School teacher in Houston, TX since graduating in 2005.

Faculty Sponsor

David Schaeffer

Recommended Citation

Fischer, Matthew and Middleton, Colin (2006) "Stabilizing a Subcritical Bifurcation in a Mapping Model of Cardiac-Membrane Dynamics," Rose-Hulman Undergraduate Mathematics Journal: Vol. 7: Iss. 2, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/13