Figure 5. Example of returning activity.

An active site A stimulates its neighbor B (red arrow) and receives back the activity three time steps later. This process involves a series of intermediate steps. Site A must pass through the refractory (s_A(t + 1) = 2) and quiescent (s_A(t + 2) = 0) states before becoming active (s_A(t + 3) = 1) again. Moreover, site B must be kept in the active state (s_B(t + 1) = 1) for at least one time step (s_B(t + 2) = 1) in order to be able to excite back the susceptible A site (s_A(t + 2) = 0). Therefore a nonzero persistence probability (1 − p_δ > 0) is fundamental for a nonzero returning probability (R > 0).