Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling

Bardet JB, Keller G (2006)

Publication Type: Journal article, Original article

Publication year: 2006

Journal

Nonlinearity Institute of Physics: Hybrid Open Access

Publisher: Institute of Physics: Hybrid Open Access

Pages Range: 2193-2210

Journal Issue: 19

DOI: 10.1088/0951-7715/19/9/012

Abstract

We construct a mixing continuous piecewise linear map on [-1, 1] with the property that a two-dimensional lattice made of these maps with a linear north and east nearest neighbour coupling admits a phase transition. We also provide a modification of this construction where the local map is an expanding analytic circle map. The basic strategy is borrowed from Gielis and MacKay (2000 Nonlinearity 13 867-88); namely, we compare the dynamics of the CML with those of a probabilistic cellular automaton of Toom's type; see MacKay (2005 Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Lecture Notes in Physics vol 671) ed J-R Chazottes and B Fernandez (Berlin: Springer) pp 65-94) for a detailed discussion. © 2006 IOP Publishing Ltd and London Mathematical Society.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

University of Rouen / Université de Rouen FR France (FR)

How to cite

APA:

Bardet, J.-B., & Keller, G. (2006). Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling. Nonlinearity, 19, 2193-2210. https://doi.org/10.1088/0951-7715/19/9/012

MLA:

Bardet, Jean-Baptiste, and Gerhard Keller. "Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling." Nonlinearity 19 (2006): 2193-2210.

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