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It is shown how different globally coupled map systems can be analyzed undera common framework by focusing on the dynamics of their respective globalcoupling functions. We investigate how the functional form of the couplingdetermines the formation of clusters in a globally coupled map system and theresulting periodicity of the global interaction. The allowed distributions ofelements among periodic clusters is also found to depend on the functional formof the coupling. Through the analogy between globally coupled maps and a singledriven map, the clustering behavior of the former systems can be characterized.By using this analogy, the dynamics of periodic clusters in systems displayinga constant global coupling are predicted; and for a particular family ofcoupling functions, it is shown that the stability condition of these clusteredstates can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR

Dynamics of coupling functions in globally coupled maps: Size, periodicity, and stability of clusters