Abstract:In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z( x, t). It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scro… Show more
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