A three-dimensional autowave turbulence
Vadim Biktashev
Institute of Mathematical Problems of Biology R.A.S.,
Pushchino, Moscow region, Russia
Autowave vortices are topological defects in autowave fields in nonlinear active media of various nature and serve as centers of self-organization 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 stabilize 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 non-decaying activity with curving, dying out and multiplication of vortex filaments, seemingly of chaotic character. This may be related to mechanisms of cardiac fibrillation.