Origin of arrhythmias in a heart model

Hiba Sheheitli, Richard Rand

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


An investigation of the nonlinear dynamics of a heart model is presented. The model compartmentalizes the heart into one part that beats autonomously (the x oscillator), representing the pacemaker or SA node, and a second part that beats only if excited by a signal originating outside itself (the y oscillator), representing typical cardiac tissue. Both oscillators are modeled by piecewise linear differential equations representing relaxation oscillators in which the fast time portion of the cycle is modeled by a jump. The model assumes that the x oscillator drives the y oscillator with coupling constant α. As α decreases, the regular behavior of y oscillator deteriorates, and is found to go through a series of bifurcations. The irregular behavior is characterized as involving a large amplitude cycle followed by a number n of small amplitude cycles. We compute critical bifurcation values of the coupling constant, αn, using both numerical methods as well as perturbations.

Original languageEnglish (US)
Pages (from-to)3707-3714
Number of pages8
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number11
StatePublished - Nov 2009
Externally publishedYes


  • Alternans
  • Arrhythmias
  • Cardiology
  • Coupled oscillators
  • Nonlinear vibrations
  • Relaxation oscillations


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