Branch Processes of Vortex Filaments and Hopf Invariant Constraint on Scroll Wave

摘要

In this paper, by making use of Duan's topological current theory, the evolution of the vortex filamentsin excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit pointsand encountering, splitting, or merging at the bifurcation points of a complex function Z(x,t). It is also shown that theHopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering)during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the 'exclusion principle'in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the'exclusion principle' is also protected by topology.