COMPLEX BEHAVIOR OF GLOBALLY COUPLED HAMILTONIAN ELEMENTS

We study the effects of global coupling on a set of elements whose ind ividual dynamics is that of a one-dimensional Hamiltonian system subje ct to a double-well symmetric potential. Since the coupled set is in t urn a Hamiltonian system, complete entrainment or synchronization is n ot possible due to the conservation of the phase-space volume. Instead , global coupling gives rise to a new kind of collective behavior, whe re the elements - initially scattered at random in the phase plane - b ecome distributed in a complex, fractal structure. We suggest that thi s form of spontaneous organization should be generic in the evolution of globally coupled Hamiltonian elements. (C) 1997 Elsevier Science B. V.