Attractor and saddle node dynamics in heterogeneous neural fields

BackgroundWe present analytical and numerical studies on the linear stability of spatially non-constant stationary states in heterogeneous neural fields for specific synaptic interaction kernels.MethodsThe work shows the linear stabiliy analysis of stationary states and the implementation of a nonlinear heteroclinic orbit.ResultsWe find that the stationary state obeys the Hammerstein equation and that the neural field dynamics may obey a saddle-node bifurcation. Moreover our work takes up this finding and shows how to construct heteroclinic orbits built on a sequence of saddle nodes on multiple hierarchical levels on the basis of a Lotka-Volterra population dynamics.ConclusionsThe work represents the basis for future implementation of meta-stable attractor dynamics observed experimentally in neural population activity, such as Local Field Potentials and EEG.

• Publication year

  2014

• Venue

  EPJ Nonlinear Biomedical Physics

• Publication date

  2014-05-09

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1140/EPJNBP17
• 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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