2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/29622We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a dynamical phase transition that is obtained on tuning the initial conditions and demonstrate universality and characterize the critical behavior. The critical state is shown to be reached in a self-organized manner on dynamically evolving the diffusion equation subjected to a mirror symmmetry transformation.4 pages, 5 EPS figures, RevTexStatistical Mechanicstext