Adaptive non-uniform cellular automaton for modelling of non-conservative processes

Authors

  • Avdeev S.A. Kuban State University, Krasnodar, Российская Федерация
  • Bogatov N.M. Kuban State University, Krasnodar, Российская Федерация

UDC

519.6:519.23:577.3

Abstract

A new class of non-uniform cellular automaton using special accumulative functions, which provide non-uniformity distribution related to traversed path, is presented in the work. This type of automaton allows to model the wide range of processes of energy and matter propagation in biology, technique, society, economics, taking into consideration the phenomena, which result depending on propagation path, in complex systems with structural abnormalities. While modelling one takes into consideration several phenomena intensity of which depends on traversed path, and their interrelations. The model allows to improve the quality of prediction of complex system malfunctions and effecciency of development methods for prediction of critical situations, connected with the system termination.

Keywords:

cellular automaton, accumulative function, complex systems, energy transfer, self-organization, autowaves

Author Infos

Stepan A. Avdeev

аспирант кафедры физики и информационных систем Кубанского государственного университета

e-mail: stepan.avdeev@pochta.ru

Nikolay M. Bogatov

д-р физ.-мат. наук, профессор кафедры физики и информационных систем Кубанского государственного университета

e-mail: bogatov@phys.kubsu.ru

References

  1. Moe G.K., Rheinboldt W.C., Abildskov J.A. A computer model of atrial fibrillation. American Heart Journal, 1964, vol. 67, no. 2, pp. 200-220.
  2. Pourhasanzade F., Sabzpoushan S.H. A new cellular automata model of cardiac action potential propagation based on summation of excited neighbors. World Academy of Science. Engineering and Technology, 2010, no. 44, pp. 917-921.
  3. Gerhardt M., Schuster H., Tyson J.J. A cellular automaton model of excitable media including curvature and dispersion. Science, 1990, no. 247, pp. 1563-1566.
  4. Markus M., Hess B. Isotropic cellular automaton for modeling excitable media. Nature, 1990, no. 347, pp. 56-58.
  5. Weimar J.R., Tyson J.J., Watson L.T. Diffusion and wave propagation in cellular automaton models of excitable media. Physica D., 1991, no. 55, pp. 309-327.
  6. FitzHugh R. Mathematical models of threshold phenomena in the nerve membrane. Bull. Math. Biophysics, 1955, no. 17, pp. 257-278.
  7. Aliev R.R., Panfilov A.V. A simple two-variable model of cardiac excitation. Chaos, Solitons and Fractals, 1996, no. 7(3), pp. 293-301.
  8. Indekeu J.O., Giuraniuc C.V. Cellular automaton for bacterial towers. Physica A: Statistical and Theoretical Physics, 2004, no. 336, pp. 14-26.
  9. Quadir F., Perr M.A., Khan K.A. Cellular automata based identification and removal of impulsive noise from corrupted images. Journal of Global Research in Computer Science, 2012, vol. 3, no. 4, pp. 17-20.
  10. Medernach D., Kowaliw T., Ryan C., Doursat R. Long-term evolutionary dynamics in heterogenous cellular automata. Proc. of the 15th annual conference on genetic and evolutionary computational conf., 2013, pp. 231-238.
  11. Sapin E., Bull L., Adamatzky A. A Genetic approach to search for glider guns in cellular automata. IEEE Congress on evolutionary computation, 2007, pp. 2456-2462.
  12. Seck-Tuoh-Mora J.C., Martinez G.J., Alonso-Sanz R., Hernandz-Romero N. Invertible behaviour in elementary cellular automata with memory. Information Sciences, 2012, vol. 199, no. 4, pp. 125-132.
  13. Jiang Z., Mangharam R. Modelling cardiac pacemaker malfunctions with the Virtual Heart Model. Conf. Proc. IEEE Med. Biol. Soc., 2011, pp. 263-266.
  14. Andreev S.Yu., Batalov R.E., Popov S.V., Kochegurov V.A., Vadutova F.A. Interoperacionnoe modelirovanie vozbuzhdenie miocarda predserdiy [Intraoperative modeling the excitation of the myocardium of the Atria]. Izvestiya Tomskogo politehnicheskogo universiteta [Bulletin of the Tomsk Polytechnic University], 2010, vol. 317, no. 5, pp. 189-194.
  15. Alonso-Sanz R., Martin M. Elementary cellular automata with memory. Complex Systems, 2003. no. 14. pp. 99-126.

Issue

Pages

14-20

Submitted

2014-10-10

Published

2015-03-26

How to Cite

Avdeev S.A., Bogatov N.M. Adaptive non-uniform cellular automaton for modelling of non-conservative processes. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, no. 1, pp. 14-20. (In Russian)