Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems

We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumomodel. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement.