Criticality of a nonconservative self-organized branching process in a stochastically dynamic population

Abstract

We describe a locally nonconservative selforganized branching process (SOBP) in a dynamic population of excitable agents driven by spontaneous excitation and deexcitation of agents. We demonstrate that the SOBP can exhibit criticality even in the absence of energy conservation as the population relaxes to a stable state where not a single agent is overstimulated. Our model generalizes the special case of locally conservative SOBP that was treated previously [Phys. Rev. Lett. 75, 4071 (1995)].