Existence and Stability of Standing Pulses in Neural Networks: II. Stability

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a nonsaturating nonlinear gain function. When two standing single-pulse solutions coexist, the small pulse is unstable, and the large pulse is stable. The large single pulse is bistable with the "all-off" state. This bistable localized activity may have strong implications for the mechanism underlying working memory. We show that dimple pulses have similar stability properties to large pulses but double pulses are unstable.

• Publication year

  2004

• Venue

  SIAM Journal on Applied Dynamical Systems

• Publication date

  2004-07-08

• Fields of study

  Biology, Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1137/040609483arXiv q-bio/0407014
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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