Phase synchronization and nonlinearity decision in the network of chaotic flows

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Abstract
The dynamics of a network of globally coupled chaotic flows is reduced to that of a single chaotic flow as the result of the phase synchronization. The mechanism of the nonlinearity decision among the flows is clarified and a simple decision rule is presented which holds in almost the entire range of the couplings and in a wide class of nonlinear flows. The key observation is that final attractors represent the ``motion of the center of mass'' of the network. The nonlinearity of the final attractors can be controlled by couplings.