Phys. Rev. E 79, 011911 (2009) - Transient Turing patterns in a neural field model

Transient Turing patterns in a neural field model

A. J. Elvin, C. R. Laing, and M. G. Roberts

Phys. Rev. E 79, 011911 – Published 20 January 2009

Abstract

We investigate Turing bifurcations in a neural field model with one spatial dimension. For some parameter values the resulting Turing patterns are stable, while for others the patterns appear transiently. We show that this difference is due to the relative position in parameter space of the saddle-node bifurcation of a spatially periodic pattern and the Turing bifurcation point. By varying parameters we are able to observe transient patterns whose duration scales in the same way as type-I intermittency. Similar behavior occurs in two spatial dimensions.

Received 12 August 2008

DOI:https://doi.org/10.1103/PhysRevE.79.011911

©2009 American Physical Society

Authors & Affiliations

A. J. Elvin^*, C. R. Laing, and M. G. Roberts

Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, NSMC, Auckland, New Zealand

^*Present address: Department of Mathematics, The Universityof Auckland, Private Bag 92019, Auckland, New Zealand. a.elvin@math.auckland.ac.nz

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Vol. 79, Iss. 1 — January 2009

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