Stability of localized patterns in neural fields

Konstantin Doubrovinski, J. Michael Herrmann

Research output: Contribution to journalLetter

6 Citations (Scopus)

Abstract

We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case was treated comprehensively by Amari 30 years ago, two-dimensional neural fields are much less understood. We derive conditions for the stability for the main classes of localized solutions of the neural field equation and study their behavior beyond parameter-controlled destabilization. We show that a slight modification of the original model yields an equation whose stationary states are guaranteed to satisfy the original problem and numerically demonstrate that it admits localized noncircular solutions. Typically, however, only periodic spatial tessellations emerge on destabilization of rotationally invariant solutions.

Original languageEnglish (US)
Pages (from-to)1125-1144
Number of pages20
JournalNeural Computation
Volume21
Issue number4
DOIs
StatePublished - Apr 1 2009

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Equations
Controlled
Activation
Cortex
Amaris

ASJC Scopus subject areas

  • Cognitive Neuroscience

Cite this

Stability of localized patterns in neural fields. / Doubrovinski, Konstantin; Herrmann, J. Michael.

In: Neural Computation, Vol. 21, No. 4, 01.04.2009, p. 1125-1144.

Research output: Contribution to journalLetter

Doubrovinski, Konstantin ; Herrmann, J. Michael. / Stability of localized patterns in neural fields. In: Neural Computation. 2009 ; Vol. 21, No. 4. pp. 1125-1144.
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