Movie 3.

Phase space trajectories of two cells with excitable periodic phase wave patterning behavior. Two-cell simulations in phase space for the periodic wave regime with k₁ = 2.3 in the absence or presence of diffusion, as showed in Fig. 3D. The trajectories of the two cells with initial values (u, v) = (±0.1, 0.0) are shown in teal colored lines, the gray points are unstable steady states and white points are stable steady states. Without diffusion (graph on the left) each cell is pushed by reaction (black arrows) into one of the stable steady states. In the presence of diffusion (graph on the right), the influence of reaction (black arrows) is counterbalanced by diffusion (green arrows) which pushes each cell onto the trajectory of the other unstable gray point creating coordinated loops. This behavior generates periodic wave patterns with spiral centers from noise as shown in Fig. 2E.