Spatially Coherent States in Fractally Coupled Map Lattices

Sridhar Raghavachari and James A. Glazier
Phys. Rev. Lett. 74, 3297 – Published 17 April 1995
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Abstract

We study coupled map lattices with a scaling form of connectivity and show that the dynamics of these systems exhibit a transition from spatial disorder to spatially uniform, temporal chaos as the scaling is varied. We numerically investigate the eigenvalue spectrum of the random matrix characterizing fluctuations from spatial uniformity, and find that the spectrum is real, bounded, and has a gap between the largest eigenvalue (corresponding to the uniform solution) and the remaining N1 eigenvalues (nonuniform solutions). The width of this gap depends on the scaling exponent. We associate the transition to the coherent state with the appearance of this gap.

  • Received 12 October 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.3297

©1995 American Physical Society

Authors & Affiliations

Sridhar Raghavachari and James A. Glazier

  • Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556

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Vol. 74, Iss. 16 — 17 April 1995

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