Bifurcation analysis of a distributed-delay Wilson–Cowan model for sleep spindle dynamics

Anca Stanoev, Anca Rădulescu, Eva Kaslik

European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

url Delayed Differential Equations Neural Networks Stability

Abstract

Sleep spindles are hallmark thalamo-cortical oscillations of non-REM sleep implicated in memory processing and emotion regulation. We develop and analyze a Wilson–Cowan mean-field model of a corticothalamo-reticular circuit comprising cortical pyramidal and inhibitory populations, thalamic relay cells, and reticular thalamic populations, to capture spindle-like dynamics at the population level. Particular emphasis is placed on neuroprocessing times within the circuit, modeled through weak Gamma-distributed delayed feedback. We study the system with and without distributed delays to determine how temporal effects interact with coupling architecture to reshape the underlying dynamics. Using stability and bifurcation analysis, we characterize the impact of delayed feedback and connectivity strengths on equilibria, oscillatory regimes, and transitions into and out of spindle-like activity. Our results show that timing acts jointly with connectivity to govern the emergence and modulation of spindle-generating dynamics. The model provides a mathematically tractable framework for investigating mechanisms underlying sleep spindle activity in thalamo-cortical networks.

BibTeX

@misc{StanoevRadulescuKaslik_ECMTB_2026,
  title         = {
    Bifurcation analysis of a distributed-delay {Wilson–Cowan} model for sleep
    spindle dynamics
  },
  author        = {Anca Stanoev and Anca Rădulescu and Eva Kaslik},
  url           = {https://contributions.ecmtb2026.org/event/1/contributions/1080},
  eventdate     = {2026-07-16},
  eventtitle    = {European Conference on Mathematical and Theoretical Biology (ECMTB 2026)},
  venue         = {University of Graz, Graz, Austria},
  type          = {Conference Poster},
  language      = {en},
  abstract      = {
    Sleep spindles are hallmark thalamo-cortical oscillations of non-REM sleep
    implicated in memory processing and emotion regulation. We develop and
    analyze a Wilson–Cowan mean-field model of a corticothalamo-reticular
    circuit comprising cortical pyramidal and inhibitory populations, thalamic
    relay cells, and reticular thalamic populations, to capture spindle-like
    dynamics at the population level. Particular emphasis is placed on
    neuroprocessing times within the circuit, modeled through weak
    Gamma-distributed delayed feedback. We study the system with and without
    distributed delays to determine how temporal effects interact with coupling
    architecture to reshape the underlying dynamics. Using stability and
    bifurcation analysis, we characterize the impact of delayed feedback and
    connectivity strengths on equilibria, oscillatory regimes, and transitions
    into and out of spindle-like activity. Our results show that timing acts
    jointly with connectivity to govern the emergence and modulation of
    spindle-generating dynamics. The model provides a mathematically tractable
    framework for investigating mechanisms underlying sleep spindle activity in
    thalamo-cortical networks.
  },
}