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 charg...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.展开更多
In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in details.By using the Duan's topological current theory,we rewrite the to...In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in details.By using the Duan's topological current theory,we rewrite the topological currentform of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum ofthe linking and self-linking numbers of the knotted RS vortices.Furthermore,the conservation of the Hopf invariant inthe splitting,the mergence and the intersection processes of knotted RS vortices is also discussed.展开更多
基金supported by National Natural Science Foundation of China and the Cuiying Programme of Lanzhou University
文摘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.
基金supported by National Natural Science Foundation of China and the Cuiying Programme of Lanzhou University
文摘In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in details.By using the Duan's topological current theory,we rewrite the topological currentform of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum ofthe linking and self-linking numbers of the knotted RS vortices.Furthermore,the conservation of the Hopf invariant inthe splitting,the mergence and the intersection processes of knotted RS vortices is also discussed.
