Microscopic model for FitzHugh-Nagumo dynamics

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 5, 1997, Pages 5657-5670

  Malevanets, Anatoly ^a   Kapral, Raymond ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BROWNIAN MOVEMENT; COMPUTER SIMULATION; DIFFUSION; MARKOV PROCESSES; MATHEMATICAL MODELS; PHASE TRANSITIONS; PROBABILITY;

BIRTH DEATH PROCESSES; FITZHUGH-NAGUMO DYNAMICS; MASS ACTION RATE LAW;

REACTION KINETICS;

EID: 0031146972     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.5657     Document Type: Article

References (31)

1. R. FitzHugh, Biophys. J.1, 445 (1961);
2. J. Nagumo, S. Arimoto and Y. Yoshikawa, Proc. IRE50, 2061 (1962).
3. See, for instance, M. Courtemanche, W. Skaggs and A T. Winfree, Physics D41, 173 (1990);
4. A T. Winfree, Chaos1, 3031 (1991);
5. A T. Winfree, SIAM Review32, 1 (1990) and references therein.
6. T. Ohta, A. Ito and A. Tetsuka, Phys. Rev. A42, 3225 (1990);
7. T. Ohta, R. Mimura and M. Kobayashi, Physica D34, 115 (1989).
8. A. Hagberg and E. Meron, Phys. Rev. Lett.72, 2494 (1994);
9. C. Elphik, A. Hagberg and E. Meron, Phys. Rev. E51, 3052 (1995).
10. D M. Petrich and R E. Goldstein, Phys. Rev. Lett.72, 1120 (1994);
11. R E. Goldstein, D J. Muraki and D M. Petrich, Phys. Rev. E53, 3933 (1996).
12. K J. Lee, W D. McCormack, Q. Ouyang and H L. Swinney, Science261, 192 (1993);
13. K J. Lee and H L. Swinney, Phys. Rev. E51, 1899 (1995);
14. K J. Lee, W D. McCormack, J. Pearson and H L. Swinney, Nature214, 215 (1994).
15. A cellular automaton model to simulate reaction-diffusion equations was constructed by J. Weimar and J P. Boon, Phys. Rev. E49, 1749 (1994)
16. and applied to the FHN model in J. Weimar, D.Sc. thesis, Brussels (1995).
17. The cellular automaton is not deduced from a microscopic dynamics.
18. See, for example, B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J D. Watson, The Molecular Biology of the Cell (Garland, New York, 1983).
19. M. Eiswirth and G. Ertl, in Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995), and references therein.
20. J P. Boon, D. Dab, R. Kapral and A. Lawniczak, Phys. Rep.273, 55 (1996).
21. U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau and J P. Rivet, Complex Syst.1, 649 (1987).
22. C W. Gardiner, Handbook of Stochastic Processes (Springer-Verlag, New York, 1985).
23. S. Chapman and T G. Cowling, Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, England, 1952).
24. P C. Hohenberg and B I. Halperin, Rev. Mod. Phys.49, 435 (1977).
25. A J. Bray and S. Puri, Phys. Rev. Lett.67, 2670 (1991);
26. H. Toyoki, Phys. Rev. B45, 1965 (1992).
27. P. Coullet, J. Lega, B. Houchmanzadeh and J. Lajzerowich, Phys. Rev. Lett.65, 1352 (1990).
28. A. Malevanets and R. Kapral, Phys. Rev. Lett.77, 767 (1996).
29. J. Gunton and M. Droz, Introduction to the Theory of Metastable and Unstable States, Vol. 183 of Lecture Notes in Physics (Springer-Verlag, New York, 1983).
30. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes (Springer-Verlag, New York, 1987).
31. N. Margolus, in Pattern Formation and Lattice-Gas Automata, edited by R. Kapral and A. Lawniczak (Fields Institute Communications, AMS, Providence, 1996), p. 165.