Hysteresis and multistability in networks of bistable stochastic elements with global interaction

We demonstrate the existence of the first-order phase transitions and hysteresis in a network of bistable stochastic elements with global interaction subject to additive white noise. Using the Fokker-Planck equation approach, we present a method which allows one to use a continuation technique (AUTO) to follow the stationary one-particle distribution density in the space of system parameters. In addition, the Gaussian approximation is employed to compute the loci of the bifurcation points.