Spiral waves in three-dimensional excitable media with light-sensitive reaction

Abstract

The propagation of spiral waves in three-dimensional excitable media with and without forcing is studied numerically, and it is shown that, when localized forcing is imposed in a cube located in the middle of the computational domain, the spiral wave preserves its integrity, although it exhibits a dent along the cube’s periphery and is unable to penetrate into the cube. However, when forcing is applied in a parallelepiped which extends across the entire domain in the vertical direction and is located in the middle of the three-dimensional excitable medium, the spiral wave is destroyed by the strip forcing and two active regions are created on either side of the strip. These active regions are characterized by high concentration of the activator, move towards the boundaries parallel to the strip, and, upon reaching them, move rather quickly in a direction parallel to the strip. They also form complex spatial patterns, e.g., ear-shaped regions, and convoluted annular regions on both sides of the strip, where the activator’s concentration is small. These spatio-temporal patterns are periodic with a period and a width which are larger than those corresponding to the localized forcing. It is also shown that strip forcing not only destroys the spiral wave, it also increases the period and width of the breathing-type motions that result from such a destruction.