Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model

Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.