Stability properties of solitary waves and periodic wave trains in a two-dimensional network of spiking neurons.

We investigate solitary waves of excitation in a two-dimensional network of spiking neurons with distance-dependent couplings. A continuum description is developed that does not require spatial or temporal averaging. Using this description, propagation velocities and dispersion relations for solitary waves and periodic wave trains can be calculated analytically. We show that the stability properties of solitary waves and wave trains are dominated by form instabilities which are genuine to the two-dimensional nature of the system.