Snakes and ladders in an inhomogeneous neural field model

Daniele Avitabile*, Helmut Schmidt

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes-and-ladders bifurcation structure. In the case of Heaviside firing rates, we construct analytically symmetric and asymmetric states and hence derive closed-form expressions for the corresponding bifurcation diagrams. We show that the approach proposed by Beck and co-workers to analyze snaking solutions to the Swift-Hohenberg equation remains valid for the neural field model, even though the corresponding spatial-dynamical formulation is non-autonomous. We investigate how the modulation amplitude affects the bifurcation structure and compare numerical calculations for steep sigmoidal firing rates with analytic predictions valid in the Heaviside limit.

Original languageEnglish
Pages (from-to)24-36
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Publication statusPublished - 15 Feb 2015
Externally publishedYes


  • Bumps
  • Inhomogeneities
  • Localized states
  • Neural fields
  • Snakes and ladders


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