Pattern formation via intermittence from microscopic deterministic dynamics

Marco Hernández, Daniel Escaff, Ricardo Finger

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We propose a one-dimensional lattice model, inspired by population dynamics interaction. The model combines a variable coupling range with the Allee effect. The system is capable of exhibiting pattern formation that is similar to what occurs in similar continuous models for population dynamics. However, the formation features are quite different; in this case the pattern emerges from a disorder state via intermittence. We analytically estimated the selected wavelength of the formed pattern and numerically studied fluctuations around the mean wavelength. We also comment on the relationship between intermittence and the edge of chaos as well as sensitivity to initial conditions. Next, we present an analytical prediction of the influence of the world size on the intermittent regime which is in good agreement with the numerical observations. Moreover, the last calculation provided us an alternative way to compute the pattern wavelength. Finally, we discuss the continuous limit of our lattice model.

Original languageEnglish
Article number056218
JournalPhysical Review E
Volume85
Issue number5
DOIs
StatePublished - 29 May 2012

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