Resonant Drift of Spiral Waves in the Complex Ginzburg-Landau Equation

Journal of Biological Physics

Volumn 25, Issue 2-3, 1999, Pages 115-127

  Biktasheva, Irina V ^a,b   Elkin, Yury E ^a   Biktashev, Vadim N ^a,b  

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

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Asymptotics; Autowaves; Oscillatory medium; Parametric drift; Reaction diffusion system; Resonant drift; Response functions; Spiral waves

Indexed keywords

EID: 0009956688     PISSN: 00920606     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1005134901624     Document Type: Article

References (16)

1. Gray, R.A. and Jalife, J.: Spiral waves and the heart, Int. J. of Bifurcation and Chaos 6 (1996), 415-435.
2. Keener, J.P.: The dynamics of 3-dimensional scroll waves in excitable media, Physica D 31 (1988), 269-276.
3. Biktashev, V.N. and Holden, A.V.: Resonant drift of autowave vortices in 2D and the effects of boundaries and inhomogeneities, Chaos, Solitons and Fractals 5 (1995), 575-622.
4. Davydov, V.A., Zykov, V.S., Mikhailov, A.S. and Brazhnik, P.K.: Drift and resonance of spiral waves in active media, Radiofizika 31 (1988), 574-582.
5. Agladze, K.I., Davydov, V.A. and Mikhailov, A.S.: Observation of a helical wave resonance in an excitable distributed medium, JETP Lett. 45 (1987), 767-770.
6. Biktashev, V.N. and Holden, A.V.: Design principles of a low-voltage cardiac defibrillator based on the effect of feed-back resonant drift, J. Theor. Biol. 169 (1994), 101-113.
7. Holden, A.V.: Defibrillation in models of cardiac muscle, J. Theoretical Medicine 1 (1997), 91-102.
8. Biktashev, V.N. and Holden, A.V.: Control of re-entrant activity in a model of mammalian atrial tissue, Proc. Roy. Soc. London B 260 (1995), 211-217.
9. Biktashev, V.N. and Holden, A.V.: Re-entrant activity and its control in a model of mammalian ventricular tissue, Proc. Roy. Soc. London B 263 (1996), 1373-1382.
10. Biktashev, V.N. and Holden, A.V.: Re-entrant waves and their elimination in a model of mammalian ventricular tissue, Chaos 8 (1998), 48-56.
11. Biktasheva, I.V., Elkin, Yu.E. and Biktashev, V.N.: Localised sensitivity of spiral waves in the Complex Ginzburg-Landau Equation, Phys. Rev. E 57 (1998), 2656-2659.
12. Noble, D., Leguennec, J.Y. and Winslow, R.: Functional roles of sodium-calcium exchange in normal and abnormal cardiac rhythm, Ann. N. Y. Acad. Sci. 779 (1996), 480-488.
13. Robinson, J.C.: Finite-dimensional behavior in dissipative partial differential equations, Chaos 5 (1995), 330-345.
14. Kuramoto, Y. and Tsuzuki, T.: On the formation of dissipative structures in reaction-diffusion systems: Reduction perturbation approach, Prog. Theor. Phys. 54 (1975), 687-699.
15. Hagan, P.S.: Spiral waves in reaction-diffusion equations, SIAM J. Appl. Math. 42 (1982), 762-786.
16. Wellner, M., Pertsov, A.M. and Jalife, J.: Spatial Doppler anomaly in an excitable medium, Phys. Rev. E 54 (1996), 1120-1125.