Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2008-07-24
Commun. Theor. Phys. 52 (2009) 1149
Nonlinear Sciences
Pattern Formation and Solitons
9 pages, 5 figures
Scientific paper
10.1088/0253-6102/52/6/31
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 $Z(\vec{x},t)$. 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 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.
Mo Shu-Fan
Ren Ji-Rong
Zhu Tianfei
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