Spiral waves in three-dimensional excitable media with light-sensitive reaction

Chaos, Solitons and Fractals

Volumn 18, Issue 2, 2003, Pages 365-373

  Ortigosa, E M ^a   Romero, L F ^a   Ramos, J I ^b  

^a Campus de Teatinos   (Spain)

^b UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; NONLINEAR EQUATIONS;

SPIRAL WAVES;

WAVE PROPAGATION;

EID: 0038558614     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00002-X     Document Type: Article

References (27)

1. Winfree A.T. The geometry of biological time. 2001;Springer-Verlag, New York.
2. Kapral R., Showalter R. Chemical waves and patterns. 1995;Kluwer Academic, Dordrecht.
3. Field R.J., Burger M. Oscillations and travelling waves in chemical systems. 1985;John Wiley & Sons, New York.
4. Holden A.V., Markus M., Othmer H.G. Nonlinear wave processes in excitable media. 1991;Plenum Press, New York.
5. Dolnik M., Zhabotinsky A.M., Epstein I.R. Resonant suppression of turing patterns by periodic illumination. Phys. Rev. E. 63:2001;026101-1-10.
6. Hwang S.-M., Choe W.G., Lee K.J. Complex dynamics of a spiral tip in the presence of an extrinsic local modulation. Phys. Rev. E. 62:2000;4799-4803.
7. Ramos J.I. Dynamics of spiral waves in excitable media with local time-periodic modulation. Chaos, Solitons & Fractals. 13:2002;1383-1392.
8. Panfilov A.V., Müller S.C., Zykov V.S., Keener J.P. Elimination of spiral waves in cardiac tissue by multiple electrical shocks. Phys. Rev. E. 61:2000;4644-4647.
9. Schebesch I., Engel H. Interacting spiral waves in the Oregonator model of light-sensitive Belousov-Zhabotinskkii reaction. Phys. Rev. E. 60:1999;6429-6434.
10. Forštová L., Ševčiková H., Marek M., Merkin J.H. Electric field effects on selectivity of reactions within propagating reaction fronts. Chem. Eng. Sci. 55:2000;233-243.
11. Ramos J.I. Wave propagation and suppression in excitable media with holes and external forcing. Chaos, Solitons & Fractals. 13:2002;1243-1251.
12. Ramos J.I. Tile patterns in excitable media subject to non-solenoidal flow fields. Chaos, Solitons & Fractals. 12:2001;2267-2281.
13. Ramos J.I. Convection-induced anisotropy in excitable media subject to solenoidal advective flow fields. Chaos, Solitons & Fractals. 12:2001;1897-1908.
14. Ramos J.I. Spatio-temporal patterns in excitable media with non-solenoidal flow straining. Math. Computers Simulation. 55:2001;607-619.
15. Ramos J.I. Propagation of spiral waves in anisotropic media: from waves to stripes. Chaos, Solitons & Fractals. 12:2001;1057-1064.
16. Markus M., Krafczyk M., Hess B. Randomized automata for isotropic modelling of two- and three-dimensional waves and spatiotemporal chaos in excitable media. Holden A.V., Markus M., Othmer H.G. Nonlinear wave processes in excitable media. 1991;161-182 Plenum Press, New York.
17. Scott S.K., Johnson B.R., Taylor A.F., Tinsley M.R. Complex chemical reactions - a review. Chem. Eng. Sci. 55:2000;209-215.
18. Aranson I., Mitkov I. Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems. Phys. Rev. E. 58:1998;4556-4559.
19. Brazhnik P.K., Tyson J.J. Velocity-curvature dependence for chemical waves in the Belousov-Zhabotinsky reaction: Theoretical explanation of experimental observations. Phys. Rev. E. 59:1999;3920-3925.
20. Winfree A.T. Stable particle-like solutions to nonlinear wave equations of three-dimensional excitable media. SIAM Rev. 32:1990;1-53.
21. Keener J.P., Tyson J.J. The dynamics of scroll waves in excitable media. SIAM Rev. 34:1992;1-39.
22. Mantel R.-M., Barkley D. Parametric forcing of scroll-wave patterns in three-dimensional excitable media. Physica D. 149:2001;107-122.
23. Yagisita H., Mimura M., Yamada M. Spiral wave behaviors in an excitable reaction-diffusion system on a sphere. Physica D. 124:1998;126-136.
24. Zuohuan Z., Tianshou Z., Zifan Z., Suochun Z. Periodic solution and global structure of Oregonator. Chaos, Solitons & Fractals. 11:2000;1191-1195.
25. Muñuzuri A.P., Pérez-Muñuzuri V., Pérez-Villar V. Attraction and repulsion of spiral waves by localized inhomogeneities in excitable media. Phys. Rev. E. 58:1998;R2689-R2692.
26. Ramos J.I. Linearization methods for reaction-diffusion equations: Multidimensional problems. Appl. Math. Comput. 88:1997;225-254.
27. Ortigosa E.M., Romero L.F., Ramos J.I. Three-dimensional simulations of spiral waves in reacting and diffusing media on DSM computers. Ingber M., Power H., Brebbia C.A. Applications of high-performance computing in engineering VI. 2000;11-20 WIT Press, Southampton, UK.