Fig. 3: Simulations of two species of RTPs when non-reciprocity survives coarse-graining.

Microscopic simulations of Eq. (15), with self-inhibition and non-reciprocal cross interactions. a and c Dynamical and static patterns observed in simulations, respectively; α-particles are depicted in red, β-particles in blue. The snapshots correspond to the larger symbols shown in (b). b Phase diagram as the couplings \({\kappa }_{\alpha }^{c}\) and \({\kappa }_{\beta }^{c}\) are varied, where we remind that \({\kappa }_{\mu }^{c}\, > \,0\) corresponds to the activation of the motility of species μ by the density of species ν, whereas \({\kappa }_{\mu }^{c}\, < \,0\) corresponds to an inhibition. The background colors correspond to the predictions of linear stability analysis which are confirmed by numerical simulations (small symbols). The phase diagram is symmetric with respect to the dashed line \({\kappa }_{\beta }^{c}={\kappa }_{\alpha }^{c}\) upon inverting the roles of α- and β-particles in (a, c). See Methods for other parameters and numerical details.