V.N. Biktashev
Institute for Mathematical Problems in Biology
Pushchino, Moscow Region, 142292, Russia
July 8, 1996; revised April 1, 1997; converted to HTML March 20, 1998
Autowave vortices are topological defects in autowave fields in nonlinear active media of various nature and serve as centers of self-organisation in the medium. In three-dimensional media, the topological defects are lines, called vortex filaments. Evolution of three-dimensional vortices, in certain conditions, can be described in terms of evolution of their filaments, analogously to that of hydrodynamical vortices in LIA approximation. In the motion equation for the filament, a coefficient called filament tension, plays a principal role, and determines qualitative long-time behaviour. While vortices with positive tension tend to shrink and so either collapse or stabilise to straight shape, depending on boundary conditions, vortices with negative tension show internal instability of shape. This is an essentially three-dimensional effect, as two-dimensional media with the same parameters do not possess any peculiar properties. In large volumes, the instability of filaments can lead to propagating, non-decremental activity composed of curved vortex filaments that multiply and annihilate in an apparently chaotic manner. This may be related to a mechanism of cardiac fibrillation.