Topological analysis of scroll wave dynamics in higher-dimensional stochastic excitable systems

Noise is inevitable in excitable reaction-diffusion systems and could affect the instability of spiral or scroll waves in low (two or three) space dimensions. This computational study explores how noise affects the scroll wave dynamics in excitable media with higher space dimensions. Numerical simulations are performed using the stochastic FitzHugh-Nagumo system with N-space dimensions (N≥4). To examine the scroll wave dynamics, algebraic topological features of excitation patterns are analyzed using the homology method. In N-dimensional excitable media, high-dimensional scroll waves rotating around (N-2)-dimensional manifolds exist. As the noise intensity level increases, the frequency of scroll-wave breakup increases, and the Betti numbers for excitation regions increase. The noise-induced scroll-wave breakup is reduced in the presence of localized non-conductive regions. The numerical simulations and homology analysis could successfully reveal noise-induced scroll wave patterns in high-dimensional reaction-diffusion systems.