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Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

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Abstract

A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.

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Authors and Affiliations

  1. Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040, Madrid, Spain

    Yongli Song, Valeri A. Makarov & Manuel G. Velarde

  2. Department of Mathematics, Tongji University, 200092, Shanghai, China

    Yongli Song

  3. Depto. de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, Avda. Complutense s/n, 28040, Madrid, Spain

    Valeri A. Makarov

Authors
  1. Yongli Song
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  2. Valeri A. Makarov
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  3. Manuel G. Velarde
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Correspondence to Valeri A. Makarov.

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Song, Y., Makarov, V.A. & Velarde, M.G. Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks. Biol Cybern 101, 147–167 (2009). https://doi.org/10.1007/s00422-009-0326-5

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  • DOI: https://doi.org/10.1007/s00422-009-0326-5

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