Persistent entanglement due to helicity conservation in excitable media

Abstract

This work addresses the topic of knotted stable structures in excitable media. These structures appear in a wide variety of situations, such as cardiac fibrillation, chemical reactions, etc. Entangled curves have been found in numerical computations of the equations that describe excitable media. They present an unusual stability. An explanation for this behaviour has been an open question. In the present work we introduce for the first time the meaning of the helicity in an excitable media as a new tool to study the stability of these systems. The helicity is related to the total entanglement of the system. We have studied how the helicity is conserved or lost through the walls of the medium and shown that these behaviours are dominated by the boundary conditions, so the distortion of these conditions could lead to the disappearance of the structures.