Unusual spiral wave dynamics in the Kessler-Levine model of an excitable medium

The Kessler-Levine model is a two-component reaction-diffusion system that describes spatiotemporal dynamics of the messenger molecules in a cell-to-cell signaling process during the aggregation of social amoeba cells. An excitation wave arising in the model has a phase wave at the wave back, which simply follows the wave front after a fixed time interval with the same propagation velocity. Generally speaking, the medium excitability and the refractoriness are two important factors which determine the spiral wave dynamics in any excitable media. The model allows us to separate these two factors relatively easily since the medium refractoriness can be changed independently of the medium excitability. For rigidly rotating waves, the universal relationship has been established by using a modified free-boundary approach, which assumes that the front and the back of a propagating wave are thin in comparison to the wave plateau. By taking a finite thickness of the domain boundary into consideration, the validity of the proposed excitability measure has been essentially improved. A novel method of numerical simulation to suppress the spiral wave instabilities is introduced. The trajectories of the spiral tip observed for a long refractory period have been investigated under a systematic variation of the medium refractoriness.