Localized sensitivity of spiral waves in the complex Ginzburg-Landau equation

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

Volumn 57, Issue 3, 1998, Pages 2656-2659

  Biktasheva, I V ^a   Elkin, Y E ^a   Biktashev, V N ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001599510     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.2656     Document Type: Article

References (11)

1. A. N. Zaikin and A. M. Zhabotinsky, Nature (London) 225, 535 (1970).NATUAS
2. M. A. Allessie, F. I. M. Bonk, and F. J. G. Schopman, Circ. Res. 32, 54 (1973).CIRUAL
3. F. Alcantara and M. Monk, J. Gen. Microbiol. 85, 321 (1974).
4. N. A. Gorelova and J. Bures, J. Neurobiol. 14, 353 (1983).
5. S. Jakubith, Phys. Rev. Lett. 65, 3013 (1990).PRLTAO
6. V. N. Biktashev and A. V. Holden, Chaos Solitons Fractals 5, 575 (1995).CSFOEH
7. J. P. Keener, Physica D 31, 269 (1988).PDNPDT
8. V. N. Biktashev, A. V. Holden, and H. Zhang, Philos. Trans. R. Soc. London, Ser. A 347, 611 (1994).PTRMAD
9. For calculations, it was convenient to keep treating Eq. (12) as a complex equation. The complexification of the linearized theory then leads to an algebra with two imaginary units, I from Eq. (12), and i of the linearized theory, with i2=I2=-1 and iI=Ii. It has divisors of zero, e.g., (i+I)(i-I)=0. We did not find in literature if it has any special name.
10. In this model, the direction of group velocity is opposite to that of phase velocity, and so proper spiral waves, with group velocity directed outwards, look converging.
11. P. S. Hagan, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 42, 762 (1982). SMJMAP