A dynamic neural field model of continuous input integration

Weronika Wojtak*, Stephen Coombes, Daniele Avitabile, Estela Bicho, Wolfram Erlhagen

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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The ability of neural systems to turn transient inputs into persistent changes in activity is thought to be a fundamental requirement for higher cognitive functions. In continuous attractor networks frequently used to model working memory or decision making tasks, the persistent activity settles to a stable pattern with the stereotyped shape of a “bump” independent of integration time or input strength. Here, we investigate a new bump attractor model in which the bump width and amplitude not only reflect qualitative and quantitative characteristics of a preceding input but also the continuous integration of evidence over longer timescales. The model is formalized by two coupled dynamic field equations of Amari-type which combine recurrent interactions mediated by a Mexican-hat connectivity with local feedback mechanisms that balance excitation and inhibition. We analyze the existence, stability and bifurcation structure of single and multi-bump solutions and discuss the relevance of their input dependence to modeling cognitive functions. We then systematically compare the pattern formation process of the two-field model with the classical Amari model. The results reveal that the balanced local feedback mechanisms facilitate the encoding and maintenance of multi-item memories. The existence of stable subthreshold bumps suggests that different to the Amari model, the suppression effect of neighboring bumps in the range of lateral competition may not lead to a complete loss of information. Moreover, bumps with larger amplitude are less vulnerable to noise-induced drifts and distance-dependent interaction effects resulting in more faithful memory representations over time.

Original languageEnglish
Pages (from-to)451-471
Number of pages21
JournalBiological Cybernetics
Issue number5
Early online date21 Aug 2021
Publication statusPublished - Oct 2021

Bibliographical note

Funding Information:
The work received financial support from FCT through the PhD fellowship PD/BD/128183/2016 the project “Neurofield” (PTDC/MAT-APL/31393/2017) and the research centre CMAT within the project UID/MAT/00013/2020.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • conservation law
  • dynamic neural field
  • input integration
  • localized states
  • stability


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