From coupled map lattices to the stochastic Kardar-Parisi-Zhang equation

Eytan Katzav; Leticia F. Cugliandolo

doi:10.1016/j.physa.2006.04.083

From coupled map lattices to the stochastic Kardar-Parisi-Zhang equation

Eytan Katzav^*, Leticia F. Cugliandolo

^*Corresponding author for this work

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

3 Scopus citations

Abstract

We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar-Parisi-Zhang growth equation and of the Fisher-Kolmogorov-Petrovskii-Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space-time behaviour is of KPZ type.

Original language	English
Pages (from-to)	96-99
Number of pages	4
Journal	Physica A: Statistical Mechanics and its Applications
Volume	371
Issue number	1
DOIs	https://doi.org/10.1016/j.physa.2006.04.083
State	Published - 1 Nov 2006
Externally published	Yes

Bibliographical note

Funding Information:
We thank very useful discussions with H. Chaté, B. Derrida, J. González, J. Kurchan, S. Majumdar, N. Mousseau, I. Procaccia, L. Trujillo and F. Zamponi, and financial support from PICS 3172. L.F.C. is a member of IUF.

Keywords

Coupled logistic maps
Lyapunov vector
Stochastic growth
Travelling waves

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abstract = "We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar-Parisi-Zhang growth equation and of the Fisher-Kolmogorov-Petrovskii-Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space-time behaviour is of KPZ type.",

keywords = "Coupled logistic maps, Lyapunov vector, Stochastic growth, Travelling waves",

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AU - Cugliandolo, Leticia F.

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PY - 2006/11/1

Y1 - 2006/11/1

N2 - We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar-Parisi-Zhang growth equation and of the Fisher-Kolmogorov-Petrovskii-Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space-time behaviour is of KPZ type.

AB - We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar-Parisi-Zhang growth equation and of the Fisher-Kolmogorov-Petrovskii-Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space-time behaviour is of KPZ type.

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KW - Lyapunov vector

KW - Stochastic growth

KW - Travelling waves

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From coupled map lattices to the stochastic Kardar-Parisi-Zhang equation

Abstract

Bibliographical note

Keywords

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