### 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 language | English |
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Pages (from-to) | 754-766 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 233 |

Issue number | 3-4 |

Publication status | Published - Dec 1 1996 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*233*(3-4), 754-766.

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

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 233, no. 3-4, pp. 754-766.

}

TY - JOUR

T1 - Complex spatiotemporal patterns in two lattice models with instability

AU - Neufeld, Zoltán

AU - Vicsek, Mária

AU - Vicsek, T.

PY - 1996/12/1

Y1 - 1996/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030405504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030405504&partnerID=8YFLogxK

M3 - Article

VL - 233

SP - 754

EP - 766

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3-4

ER -