An analytical velocity field of spiral tips in reaction-diffusion systems

Spiral waves are ubiquitous in diverse physical, chemical, and biological systems. The tip (phase singularity) of a spiral wave is considered to represent its organizing center. Here, we derive an analytical velocity field of spiral tips based on the variables of a general two-variable reaction-diffusion (RD) equation. From this velocity field, we can predict the velocities of spiral tips at timetas long as the values of the variables are given at that time. Numerical simulations with two-variable RD models are in quantitative agreement with the analytical results. Furthermore, we also demonstrate the velocity field of spiral tips in the Luo-Rudy model for cardiac excitation.