Origin of arrhythmias in a heart model
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...
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| التنسيق: | article |
| منشور في: |
2009
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/6291 https://doi.org/10.1016/j.cnsns.2009.03.016 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php http://www.sciencedirect.com/science/article/pii/S100757040900152X |
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| الملخص: | 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. |
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