Emergent symmetry breaking during the foraging collective activity by ants

This study analyzes a system of nonlinear differential equations associated with the number of foraging ants visiting two identical exploitation sources in a static environment. Steady-state solutions correspond to establishing pheromone trails sustained after the colony density reaches a critical size. In the quasi-steady-state approximation, the model reduces to a single-variable symmetry description. After including additive white noise perturbations, the scheme becomes a Langevin equation. Solutions to this equation suggest that the processes underlying the collective task are associated with an order (recruitment-abandonment) - disorder (successful exploration) parameter that varies as a rational homographic function concerning the control parameter of the model. We find that intrinsic random disturbances, produced by successful foragers, break the symmetry of an equal number of ants in each option, leading to preferential visits to one of the two food sources. We also observe that the behavior of the order-disorder parameter strongly depends on changes in the colony size. In general, the stability of consensus in collective decision-making increases with increasing noise intensity.