Emergence of chaos in asymmetric networks

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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.

Original languageEnglish
Pages (from-to)4844-4847
Number of pages4
JournalPhysical Review Letters
Issue number23
StatePublished - 1996


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