Persistent tangles of vortex rings in excitable media

Abstract Vortex filaments in numerical excitable media form ‘stable organizing centers’: compact, spatially symmetric, temporally periodic configurations of linked and knotted rings emitting scroll-shaped wave trains while slowly moving through the medium. All past examples use excitable media in which the 2-dimensional (2d) spiral wave pivots rigidly without meander, and only one local state variable diffuses. Vortex filaments in such special media remain motionless when uncurved and free of ‘twist’. Are these conditions essential for persistence of vortex rings against collapse and reversion to a spatially uniform steady state? This paper shows by example that even if all variables diffuse (equally in this case) or if the 2d vortex ‘meanders’ spontaneously (the usual case), compact organizing centers of topologically distinct kinds can still persist. These ‘persistent organizing centers’ are not ‘stable’: they continually change shape without ever repeating. But their persistence for 70 rotation periods or more under generic conditions in numerical experiments suggests that they should be observable in nature.