Complex behavior of globally coupled Hamiltonian elements

We study the effects of global coupling on a set of elements whose individual dynamics is that of a one-dimensional Hamiltonian system subject to a double-well symmetric potential. Since the coupled set is in turn a Hamiltonian system, complete entrainment or synchronization is not possible due to the conservation of the phase-space volume. Instead, global coupling gives rise to a new kind of collective behavior, where the elements — initially scattered at random in the phase plane — become distributed in a complex, fractal structure. We suggest that this form of spontaneous organization should be generic in the evolution of globally coupled Hamiltonian elements