Self-organizing criticality and the method of automatic search of critical points

Abstract

We discuss the method of automatic search of critical point (MASCP) in the context of self-organizing criticality (SOC). The system analyzed is a contact process that presents a non-equilibrium phase transition between two states: active state and inactive state (the so-called absorbing state). The lattice sites represent infected and healthy individuals. We apply the technique MASCP to the propagation of epidemy in an unidimensional lattice at the criticality (space-domain). We take the thechnique MASCP to study SOC behavior. The time-series of density of infected individuals is analyzed using two complementary tools: Fourier analysis and detrended fluctuation analysis. We find numeric evidence that the time evolution that drives the system to the critical point in MASCP is not a SOC problem, but Gaussian noise. A SOC problem is characterized by an interaction-dominated system that goes spontaneously to the critical point. In fact MASCP goes by itself to a stationary point but it is not an interaction-dominated process, but a mean-field interaction process.