Two interacting ants.

The ants follow dynamics of Eq (10) where the stochastic switching between the states follows transition rates with and the same as for the single ant in Fig 4 and the interaction strength . The interaction with a kernel ψ(d) = e^−d2 modulates the rates multiplicatively by a factor which increases all transition rates when ants are close to each other and leaves them unchanged when they are sufficiently distant. (A) Short stochastic simulation of two interacting ants, showing also the instantaneous transition rates from the current state. The interaction modulating factor exp(0.5ψ(d)) is shown together with other transition rates (green) using the same axis. (B) The first and the second rows show the inferred transition rates (dots) for the parameters α⁽¹⁾ and α⁽²⁾, respectively, compared with the exact rates (solid curves). The inference is based on 500 simulated trajectories, each for T ∈ [0, 500]. We used the tiling functions in the z and Δz = z_n − z_n′ space and a penalization function of the form to enforce vanishing interaction outside of the range |Δz| > 2. Penalization term also avoids a degeneracy of the rates, ensuring existence of a unique solution of the inference problem.