Medium inhomogeneities modulate emerging spiral waves

We study the spatiotemporal dynamics of spiral waves in a lattice of chemically coupled memristive FitzHugh–Nagumo neurons. We also introduce local and global functional inhomogeneities by means of variations in nodal action potentials that are distributed in different ways. We find that, in the presence of globally distributed random inhomogeneity, increasing the maximum threshold for excitability generates neurons with reduced depolarization capacity. Although such a setup makes the entire medium less excitable and thus challenges the robustness of emerging spiral waves, highly excitable neurons can compensate for the less excitable ones, thereby nonetheless preserving the spiral wave pattern. However, this compensatory mechanism has limitations, which can ultimately lead to the elimination of spiral waves under specific conditions. When inhomogeneities are local, two different scenarios are possible. If the distribution is random, the spiral tip cannot penetrate the inhomogeneous region but remains resilient against it. The tip is consistently anchored to the inhomogeneity, meandering around its boundary. As the inhomogeneity size increases, the curvature of the spiral tip and the propagation speed of the circular wavefronts decrease. If the distribution is uniform, inhomogeneities are analogous to semi-conducting barriers, thus permitting the spiral rotor to penetrate while sacrificing the strength of its wavefronts.