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 Nδ 1/2<=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 Nδ modes encoded in the weights was confirmed numerically.
|Number of pages||4|
|Journal||Physical Review Letters|
|State||Published - 1996|