The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave

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 $Z(\vec{x},t)$. 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.

9 pages, 5 figures

References in corpus (8)

• On the Stability of Knots in Excitable Media
• Inner topological structure of Hopf invariant
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• Topology of Knotted Optical Vortices
• Topological Properties of Spatial Coherence Function
• The Bifurcation Theory of Magnetic Monopoles in a Charged Two-Condensate Bose-Einstein System
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