Complex spatiotemporal patterns in two lattice models with instability

Zoltán Neufeld, Mária Vicsek, T. Vicsek

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we consider two lattice models: (i) the discretized version of a simple nonlinear partial differential equation (PDE) with a singular term and (ii) a coupled map lattice (CML) with unstable coupling. Both systems are defined by simple iteration rules involving the nearest-neighbour grid points of the corresponding one-dimensional lattice. We show numerically that these models result in an apparently stochastic spatiotemporal behaviour and exhibit interesting regimes as the function of the parameters of the models. In particular, we find that by varying the relative weight B of the singular term in the PDE the total width of the solution scales with B. The CML leads to an intermittent behaviour between structured and turbulent regimes.

Original languageEnglish
Pages (from-to)754-766
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume233
Issue number3-4
Publication statusPublished - Dec 1 1996

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Coupled Map Lattices
Spatio-temporal Patterns
Lattice Model
Term
Nonlinear Partial Differential Equations
partial differential equations
Nearest Neighbor
Partial differential equation
Unstable
Grid
Iteration
Model
iteration
grids

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Complex spatiotemporal patterns in two lattice models with instability. / Neufeld, Zoltán; Vicsek, Mária; Vicsek, T.

In: Physica A: Statistical Mechanics and its Applications, Vol. 233, No. 3-4, 01.12.1996, p. 754-766.

Research output: Contribution to journalArticle

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