Dynamics of globally coupled bistable elements

The macroscopic dynamics of a large set of globally coupled, identical, noiseless, bistable elements is analytically and numerically studied. Depending on the value of the coupling constant and on the initial condition, all the elements can either evolve towards the same individual state or become divided into two groups, which approach two different states. It is shown that at a critical value of the coupling constant the system undergoes a transition from bistable evolution, where the two behaviors described above can occur, to coherent evolution, where the convergence towards the same individual state is the only possible behavior. Connections of this system with the real Ginzburg-Landau equation and with the sociological problem of opinion formation are discussed.