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Complex behavior of globally coupled Hamiltonian elements

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Zanette,  Damián H.
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Mikhailov,  Alexander S.
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Citation

Zanette, D. H., & Mikhailov, A. S. (1997). Complex behavior of globally coupled Hamiltonian elements. Physics Letters A, 235(2), 135-138. doi:10.1016/S0375-9601(97)00619-1.


Cite as: https://hdl.handle.net/21.11116/0000-0008-B672-A
Abstract
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.