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Attractor and saddle node dynamics in heterogeneous neural fields

Abstract : We present analytical and numerical studies on the linear stability of spatially non-constant stationary states in heterogeneous neural elds for speci c synaptic interaction kernels. We nd that the stationary state obeys the Hammerstein equation and that the neural eld dynamics may obey a saddle-node bifurcation. Moreover our work takes up this nding 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.
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Submitted on : Tuesday, May 6, 2014 - 5:35:06 PM
Last modification on : Monday, June 15, 2020 - 12:00:33 PM
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Peter Beim Graben, Axel Hutt. Attractor and saddle node dynamics in heterogeneous neural fields. EPJ Nonlinear Biomedical Physics, EDP Sciences, 2014, 2, pp.4. ⟨10.1140/epjnbp17⟩. ⟨hal-00987789⟩



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