Abstract
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.
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Cain, J.W. Criterion for stable reentry in a ring of cardiac tissue. J. Math. Biol. 55, 433–448 (2007). https://doi.org/10.1007/s00285-007-0100-z
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DOI: https://doi.org/10.1007/s00285-007-0100-z