A Three-Dimensional Autowave Turbulence

Autowave vortices are topological defects in autowave fields in nonlinear active media of various natures 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 behavior. While vortices with positive tension tend to shrink and so either collapse or stabilize to a 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, nondecremental 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.