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Dynamics of coupled maps with a conservation law

Grigoriev, R. O. and Cross, M. C. (1997) Dynamics of coupled maps with a conservation law. Chaos, 7 (2). pp. 311-330. ISSN 1054-1500. doi:10.1063/1.166222.

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A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are calculated for a set of independent order parameters. Numerical evidence is produced suggesting that the singularity in the density of Lyapunov exponents at lambda = 0 is a reflection of the singularity in the density of Fourier modes (a "Van Hove" singularity) and disappears if the conservation law is broken. Applicability of the Lyapunov dimension to the description of spatiotemporal chaos in a system with a conservation law is discussed.

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Additional Information:©1997 American Institute of Physics. (Received 19 August 1996; accepted 21 January 1997) R.O.G. would like to thank Professor N. R. Corngold for many helpful discussions. The authors gratefully acknowledge the support of the National Science Foundation under Grant No. DMR9013984.
Subject Keywords:chaos; phase transformations; conservation laws; dynamics; Lyapunov methods
Issue or Number:2
Record Number:CaltechAUTHORS:GRIchaos97
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6072
Deposited By: Archive Administrator
Deposited On:16 Nov 2006
Last Modified:08 Nov 2021 20:30

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