We model electrical wave propagation in a ring of cardiac tissue using an mth-order difference equation, where m denotes the number of cells in the ring. Under physiologically reasonable assumptions, the difference equation has a unique equilibrium solution. Applying Jury’s stability test, we prove a theorem concerning the local asymptotic stability of this equilibrium solution. Our results yield conditions for sustained reentrant tachycardia, a type of cardiac arrhythmia.
Copyright © 2007 Springer.
The definitive version is available at: http://link.springer.com/article/10.1007/s00285-007-0100-z
Cain, John W. "Criterion for Stable Reentry in a Ring of Cardiac Tissue." Journal of Mathematical Biology 55, no. 3 (2007): 433-448. doi:10.1007/s00285-007-0100-z.
Cain, John W., "Criterion for Stable Reentry in a Ring of Cardiac Tissue" (2007). Math and Computer Science Faculty Publications. 66.