GLOBAL DYNAMICS IN NETWORKS OF 1D ELEMENTS WITH TIME DELAYED MEAN FIELD COUPLING SUBJECT TO NOISE: SYNCHRONIZATION THRESHOLD, MULTISTABILITY AND HYSTERESIS - POTOTSKY, A.; JANSON, N. (International journal of bifurcation and chaos in applied sciences and engineering, 2010)
We determine the boundary of the synchronization domain of a large number of one-dimensional continuous stochastic elements with time delayed nonhomogeneous mean-field coupling. The exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker–Planck equation. Here the synchronization threshold is found by solving this BVP using the continuation technique (AUTO). Approximate analytics is obtained using expansion into eigenfunctions of the stationary Fokker–Planck operator. Multistability and hysteresis are demonstrated for the case of bistable elements with a polynomial potential.