Limit cycles by FEM for a one-parameter dynamical system associated to the Luo-Rudy I model
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2011
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| _version_ | 1866914779373764608 |
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| author | Bichir, Cătălin Liviu Georgescu, Adelina Amuzescu, Bogdan Nistor, Gheorghe Popescu, Marin Flonta, Maria-Luiza Corlan, Alexandru Dan Svab, Istvan |
| author_facet | Bichir, Cătălin Liviu Georgescu, Adelina Amuzescu, Bogdan Nistor, Gheorghe Popescu, Marin Flonta, Maria-Luiza Corlan, Alexandru Dan Svab, Istvan |
| contents | An one-parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system. A finite element method time approximation (FEM) is used in order to formulate the approximate problem. Starting from a Hopf bifurcation point, approximate limit cycles are obtained, step by step, using an arc-length-continuation method and Newton's method. Some numerical results are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1110_4307 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Limit cycles by FEM for a one-parameter dynamical system associated to the Luo-Rudy I model Bichir, Cătălin Liviu Georgescu, Adelina Amuzescu, Bogdan Nistor, Gheorghe Popescu, Marin Flonta, Maria-Luiza Corlan, Alexandru Dan Svab, Istvan Numerical Analysis 37N25, 37G15, 37M20, 65L60, 90C53, 37J25 An one-parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system. A finite element method time approximation (FEM) is used in order to formulate the approximate problem. Starting from a Hopf bifurcation point, approximate limit cycles are obtained, step by step, using an arc-length-continuation method and Newton's method. Some numerical results are presented. |
| title | Limit cycles by FEM for a one-parameter dynamical system associated to the Luo-Rudy I model |
| topic | Numerical Analysis 37N25, 37G15, 37M20, 65L60, 90C53, 37J25 |
| url | https://arxiv.org/abs/1110.4307 |