Evolution of the Spiral Waves in Excitable System

Details Evolution of the Spiral Waves in Excitable System Evolution of the Spiral Waves in Excitable System

2008-11-03

arxiv.org/abs/0811.0217v1

Commun. Theor. Phys. 51 (2009) 621-626

Nonlinear Sciences

Pattern Formation and Solitons

7 pages, 5 figures

Scientific paper

10.1088/0253-6102/51/4/09

Spiral wave, whose rotation center can be regarded as a point defect, widely exists in various two dimensional excitable systems. In this paper, by making use of \emph{Duan's topological current theory}, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.

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