Topological Constraints on Scroll and Spiral Waves in Excitable Media
ZHANG Hong1,2,, HU Bambi 2,3, LI Bing-Wei1, DUAN Yi-Shi4
1Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 3100272Department of Physics, and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong BaptistUniversity, Hong Kong3Department of Physics, University of Houston, Houston, TX 77204-5005, USA 4Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000
Topological Constraints on Scroll and Spiral Waves in Excitable Mediac
1Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 3100272Department of Physics, and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong BaptistUniversity, Hong Kong3Department of Physics, University of Houston, Houston, TX 77204-5005, USA 4Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000
摘要A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.
Abstract：A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.
[1] For examples, see Cross M C and Hohenberg P C 1993 Rev.Mod. Phys. 65 851 and references therein [2] Davidenko J M et al 1992 Nature 355 349 [3] Jakubith S et al 1990 Phys. Rev. Lett. 65 3013 [4] Winfree A T 1972 Science 175 634 Ouyang Q et al 2000 Phys. Rev. Lett. 84 1047 [5] Vinson M et al 1997 Nature 386 477 [6] Alonso S et al 2003 Science 299 1722 [7] Zhang H, Cao Z, Wu N J, Ying H P and Hu G 2005 Phys.Rev. Lett. 94 188301 Cao Z et al 2006 Europhys. Lett. 75 875 [8] Winfree A T 1974 Sci. Am. 230 82 [9] Agladze K I and Krinsky V I 1982 Nature 296 424 [10] Winfree A T and Strogatz S H 1983 Physica D 8 35 [11] Nandapurkar P J and Winfree A T 1987 Physica D 29 69 [12] Zykov V S 1987 Simulation of Wave Processes inExcitable Media (New York: Manchester University Press) [13] Winfree A T 1987 When Time Breaks Down(Princeton: Princeton University Press) [14] Winfree A T 1990 SIAM Rev. 32 1 [15] Winfree A T 2001 The Geometry of Biological Time2nd ed (Berlin: Springer) [16] Keener J P and Tyson J J 1992 SIAM Rev. 34 1 [17] Winfree A T 1994 Nature 371 233 [18] Gray R A et al 1998 Nature 392 75 [19] Pertsov A M et al 2000 Phys. Rev. Lett. 842738 [20] Duan Y S and Zhang H 1999 Phys. Rev. E 60 2568 [21] Wellner M et al 1999 Phys. Rev. E 59 5192 [22] Jahnke W et al 1989 J. Phys. Chem. 93 740 [23] Zhang H, Hu B, Hu G and Xiao J 2003 J. Chem. Phys. 119 4468 Zhang H, Wu N J, Ying H P, Hu G and Hu B 2004 J. Chem.Phys. 121 7276 Chen J X, Zhang H and Li Y Q 2005 J. Chem. Phys. 124 014505 [24] Barkley D 1991 Physica D 49 61
2007, Vol. 24 
