Synchronization and chaos in networks of coupled maps in application to modeling of cardiac dynamics

 pdf (1843K)  / Annotation

List of references:

  1. D. Noble. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potential // / J. Physiol. — 1962. — V. 160. — P. 317–352. — DOI: 10.1113/jphysiol.1962.sp006849.
  2. G. W. Beeler, H. Reuter. Reconstruction of the action potential of ventricular myocardial fibers // J. Physiol. — 1977. — V. 268. — P. 177–210. — DOI: 10.1113/jphysiol.1977.sp011853.
  3. C. H. Luo, Y. Rudy. A model of the ventricular cardiac action potential, depolarization, repolarization and their interaction // Circ. Res. — 1991. — V. 68. — P. 1501–1526. — DOI: 10.1161/01.RES.68.6.1501.
  4. M. Courtemanche, R. J. Ramirez, S. Nattel. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model // Am. J. Physiol. — 1998. — V. 275. — P. H301–H321.
  5. O. Bernus, R. Wilders, C. W. Zemlin, H. Verschelde, A. V. Panfilov. A computationally efficient electrophysiological model of human ventricular cells // Am. J. Physiol. — 2002. — V. 282. — P. H2296–H2308.
  6. K. H. Ten Tusscher, D. Noble, P. J. Noble, A. V. Panfilov. A model for human ventricular tissue // Am. J. Physiol. — 2004. — V. 286. — P. H1573–H1589.
  7. H. Zhang, A. V. Holden, I. Kodama, H. Honjo, M. Lei, T. Varghese, M. R. Boyett. Mathematical models of action potential in the periphery and center of the rabbit sinoatrial node // Am. J. Physiol. — 2000. — V. 279. — P. H397–H421. — DOI: 10.1152/ajpcell.2000.279.4.C1024.
  8. Y. Kurata, I. Hisatome, S. Imanishi, T. Shibamoto. Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell // Am. J. Physiol. — 2002. — V. 283. — P. H2074–H2101. — DOI: 10.1152/ajpheart.00900.2001.
  9. B. Ibarz, J. M. Casado, M. A. F. Sanjuan. Map-based models in neuronal dynamics // Phys. Rep. — 2011. — V. 501. — P. 1–74. — DOI: 10.1016/j.physrep.2010.12.003. — ads: 2011PhR...501....1I.
  10. А. К. Гренадер. Антиаритмики — блокаторы ионных каналов. Механизмы действия и структура. — Пущино: ОНТИ НЦБИ АН СССР, 1987. — 63 с.
  11. M. E. Mangoni, J. Nargeot. Genesis and Regulation of the Heart Automaticity // Physiol. Rev. — 2008. — V. 88. — P. 919–982. — DOI: 10.1152/physrev.00018.2007.
  12. А. Г. Камкин, А. А. Каменский. Фундаментальная и клиническая физиология. — учебник для студ. высш. учеб. заведений. — М: Издательский центр Академия, 2004. — 1072 с.
  13. А. Ю. Лоскутов, А. С. Михайлов. Основы теории сложных систем. — М.–Ижевск: Институт компьютерных исследований, 2007. — 620 с.
  14. J. Jalife, R. A. Gray, G. E. Morley, J. M. Davidenko. Self-organization and the dynamical nature of ventricular fibrillation // Chaos. — 1998. — V. 8. — P. 79–93. — DOI: 10.1063/1.166289. — ads: 1998Chaos...8...79J.
  15. A. V. Panfilov. Spiral breakup as a model of ventricular fibrillation // Chaos. — 1998. — V. 8. — P. 57–64. — DOI: 10.1063/1.166287. — ads: 1998Chaos...8...57P.
  16. R. W. Joyner, R. Wilders, M. B. Wagner. Propagation of pacemaker activity // Med. Bio. Eng. Comput. — 2007. — V. 45. — P. 177–187. — DOI: 10.1007/s11517-006-0102-9.
  17. M. R. Boyett, H. Honjo, I. Kodama. The sinoatrial node, a heterogeneous pacemaker structure // Cardiovasc. Res. — 2000. — V. 47. — P. 658–687. — DOI: 10.1016/S0008-6363(00)00135-8.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"