Spiral wave meander and symmetry of the plane

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 12 A/B, 1996, Pages 2433-2440

  Biktashev, V N ^a,b   Holden, A V ^b   Nikolaev, E V ^a,b  

^a INSTITUTE OF MATHEMATICAL PROBLEMS OF BIOLOGY   (Russian Federation)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001068349     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218127496001582     Document Type: Article

References (30)

1. Afrajmovich, V. S. & Shilnikov, L. P. [1983] "Invariant two-dimensional tori, their breakup and stochasticity," in Methods of Qualitative Theory of Differential Equations, eds. Bautin et al. (Gorkii University, Gorkii (in Russian)), pp. 3-26.
2. Anosov, D. V. & Arnold, V. I. (eds.) [1985] Dynamical Systems I (Springer, Berlin).
3. Barkley, D. [1994] "Euclidean symmetry and the dynamics of rotating spiral waves," Phys. Rev. Lett. 72, 164-167.
4. Barkley, D., Kness, M. & Tuckerman, L. S. [1990] "Spiral wave dynamics in a simple model of excitable media - the transition from simple to compound rotation," Phys. Rev. A42, 2489-2492.
5. Biktashev, V. N. & Holden, A. V. [1995] "Resonant drift of autowave vortices in 2D and effect of boundaries and inhomogeneities," Chaos Solitons and Fractals 5, 575-622.
6. Biktashev, V. N. & Holden, A. V. [1996] "Re-entrant activity and its control in a model of mammalian ventricular tissue," Proc. Roy. Soc. London B 263, 1373-1382.
7. Brindley, J. & Gray, P. (eds.) [1994] "Nonlinear phenomena in excitable media," Phil. Trans. Roy. Soc. London A347, 599-727.
8. Diks, C., Hoekstra, B. & Degoede, J. [1995] "Spiral wave dynamics," Chaos Solitons and Fractals 5, 645-660.
9. Efimov, I. R., Krinsky, V. I. & Jalife, J. [1995] "Dynamics of rotating vortices in the Beeler-Reuter model of cardiac tissue," Chaos Solitons and Fractals 5, 513-526.
10. Fiedler, B. [1995] "Meandering spirals," Lecture given at the Workshop on Dynamics and Symmetry, Cambridge, UK, 30 Oct-3 Nov.
11. Golubitsky, M., LeBlanc, V. G. & Melbourne, I. [1996] "Meandering of the spiral tip: An alternative approach," Dept. of Math. University of Houston, preprint 1-19.
12. Grill, S., Zykov, V. S. & Müller, S. C. [1995] "Feedback-controlled dynamics of meandering spiral waves," Phys. Rev. Lett. 75, 3368-3371.
13. Gray, R. A. & Jalife, J. [1996] "Spiral waves and the heart," Int. J. Bifurcation and Chaos 6, 415-435.
14. Holden, A. V., Markus, M. & Othmer, H. G. (eds.) [1991] Nonlinear Wave Processes in Excitable Media (Plenum, New York).
15. Janke, W., Skaggs, W. E. & Winfree, A. T. [1989] "Chemical vortex dynamics in the Belousov-Zhabotinsky reaction and in the 2-variable Oregonator model," J. Phys. Chem. 93, 740-749.
16. Karma, A. [1990] "Meandering transition in 2-dimensional excitable media," Phys. Rev. Lett. 65, 2824-2827.
17. Mantel, R. M. & Barkley, D. [1996] "Periodic forcing of spiral waves in excitable media," Phys. Rev. E 54, 4791-4801.
18. Müller, S. C. & Zykov, V. S. [1994] "Simple and complex spiral wave dynamics," Phil. Trans. Roy. Soc. London A347, 677-685.
19. Nagy-Ungvarai, Z., Ungvarai, J. & Müller, S. C. [1993] "Complexity of spiral wave dynamics," Chaos 3, 15-19.
20. Plesser, T. & Müller, K.-H. [1995] "Fourier analysis of the complex motion of spirals tips inexcitable media," Int. J. Bifurcation and Chaos 5, 1071-1084.
21. Rand, D. [1982] "Dynamics and symmetry. Predictions for modulated waves in Rotating fluids," Arch. Rational Mech. Anal. 72, 1-37.
22. Renardy, M. [1982] "Bifurcation from rotating waves," Arch. Rational Mech. Anal. 72, 49-84.
23. Steinbock, O., Zykov, V. & Müller, S. C. [1993] "Control of spiral wave dynamics in active media by periodic modulation of excitability," Nature 366, 322-324.
24. Swinney, H. L. & Krinsky, V. I. (eds.) [1991] "Waves and patterns in chemical and biological media," Physica D 49, 1-255.
25. Winfree, A. T. [1973] "Scroll-shaped waves of chemical activity in three dimensions," Science 181, 937-939.
26. Winfree, A. T. [1991] "Varieties of spiral wave behaviour - an experimentalist's approach to the theory of excitable media," Chaos 1, 303-334.
27. Wulff, C. [1996a] "Bifurcation Theory of Meandering Spiral Waves," in Nonlinear Physics of Complex Systems - Current Status and Future Trends, eds. Parisi, Z. Müller, S. C. and Zimmermann, W. (Springer-Verlag, Berlin) (to appear).
28. Wulff, C. [1996b] "Theory of meandering and drifting spiral waves in reaction-diffusion systems," Ph.D. Thesis, Fachbereich Mathematik und Informatik, Freie Universität, Berlin.
29. Zaikin, A. N. & Zhabotinsky, A. M. [1970] "Concentration wave propagation in two-dimensional liquid-phase self-oscillating system," Nature 225, 535-537.
30. Zykov, V. S. [1986] "Cycloidal circulation of spiral waves in excitable medium," Biofizika 31, 862-865.