The dynamics of a network of N nonlinear elements interacting via random asymmetric weights is studied analytically. A transition from an ordered phase to a chaotic one is obtained when the number of relevant modes used to construct the weights exceeds N^δ1/2≤δ≤1. In the ordered phase the dynamics of each element is characterized by an embedding dimension equal to one, or is dominated by one Fourier component. The transition to chaos reflecting that N coupled elements cannot follow more than N^δ modes encoded in the weights was confirmed numerically.
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Ido Kanter (1996) studied this question.
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