Clustering and synchronization with positive Lyapunov exponents

Details Clustering and synchronization with positive Lyapunov exponents Clustering and synchronization with positive Lyapunov exponents

1998-12-18

arxiv.org/abs/adap-org/9812004v1

Physics Letters A 257 (1999) 132

Nonlinear Sciences

Adaptation and Self-Organizing Systems

10 pages Latex, 2 ps figures

Scientific paper

10.1016/S0375-9601(99)00319-9

Clustering and correlation effects are frequently observed in chaotic systems in situations where, because of the positivity of the Lyapunov exponents, no dimension reduction is to be expected. In this paper, using a globally coupled network of Bernoulli units, one finds a general mechanism by which strong correlations and slow structures are obtained at the synchronization edge. A structure index is defined, which diverges at the transition points. Some conclusions are drawn concerning the construction of an ergodic theory of self-organization.

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