Emergence of chaos in asymmetric networks

I. Kanter

doi:10.1103/PhysRevLett.77.4844

Emergence of chaos in asymmetric networks

I. Kanter

Department of Physics

Research output: Contribution to journal › Article › peer-review

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Abstract

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^δ 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 N^δ modes encoded in the weights was confirmed numerically.

Original language	English
Pages (from-to)	4844-4847
Number of pages	4
Journal	Physical Review Letters
Volume	77
Issue number	23
DOIs	https://doi.org/10.1103/PhysRevLett.77.4844
State	Published - 1996

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10.1103/PhysRevLett.77.4844

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abstract = "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.",

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AB - 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.

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Emergence of chaos in asymmetric networks

Abstract

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