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

Abstract

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 time t as 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.

Keywords

• spiral waves
• pattern formation
• reaction–diffusion system