Pattern formation in a network of excitatory and inhibitory cells with adaptation

Rodica Curtu; Bard Ermentrout

doi:10.1137/030600503

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Pattern formation in a network of excitatory and inhibitory cells with adaptation

Journal article

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Peer reviewed

Pattern formation in a network of excitatory and inhibitory cells with adaptation

Rodica Curtu and Bard Ermentrout

SIAM journal on applied dynamical systems, Vol.3(3), pp.191-231

2004

DOI: 10.1137/030600503

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Abstract

A bifurcation analysis of a simplified model for excitatory and inhibitory dynamics is presented. Excitatory cells are endowed with a slow negative feedback and inhibitory cells are assumed to act instantly. This results in a generalization of the Hansel-Sompolinsky model for orientation selectiv- ity. Normal forms are computed for the Turing-Hopf instability, where a new class of solutions is found. The transition from stationary patterns to traveling waves is analyzed by deriving the normal form for a Takens-Bogdanov bifurcation. Comparisons between the normal forms and numerical solutions of the full model are presented.

Details

Title: Subtitle: Pattern formation in a network of excitatory and inhibitory cells with adaptation
Creators: Rodica Curtu
Bard Ermentrout
Resource Type: Journal article
Publication Details: SIAM journal on applied dynamical systems, Vol.3(3), pp.191-231
DOI: 10.1137/030600503
ISSN: 1536-0040
eISSN: 1536-0040
Language: English
Date published: 2004
Academic Unit: Iowa Neuroscience Institute; Mathematics
Record Identifier: 9983986086902771

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