Evolution of Spiral Waves in Excitable Systems

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of 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.