Anomalous collective dynamics of auto-chemotactic populations*

Various non-equilibrium systems that are subject to local interactions are known to exhibit collective behavior in the form of scale invariance. A prominent example are absorbing state phase transitions, which often fall into the universality class of directed percolation. Inspired by insights from equilibrium phase transitions, where long-ranged interactions tend to change the collective behavior, we want to study their influence on non-equilibrium systems. For this purpose we investigate a system of reproducing agents that are subject to limited resources and long-ranged chemotactic interactions in the form of Keller-Segel type dynamics. Close to the extinction threshold, a perturbative renormalization group analysis reveals distinct universality classes for attractive and repulsive interactions. We present the adapted phase diagram as well as a a novel nonlinear mechanism that could stabilize the continuous transition against a pattern forming instability.