Dynamics of Infinite Networks of Theta Neurons with Delays

Alexandru Fikl, Lavinia Fildan, Eva Kaslik, Raluca Mureșan

Fifth International Nonlinear Dynamics Conference (NODYCON 2026)

url Chaos synchronization Bifurcations Delayed dynamics

Abstract

We study an infinite all-to-all coupled network of identical theta neurons with synaptic interactions subject to distributed delays. Using the Watanabe–Strogatz transformation, linearization, and a characteristic equation expressed via the Laplace transform of the delay kernel, we analyze the local stability of equilibria and the effect of delays on macroscopic dynamics. We investigate whether different types of distributed delays may influence equilibrium stability and induce bifurcations. Numerical simulations support the analysis and reveal that delay effects on the global phase portrait are strongly parameter dependent, producing substantial qualitative changes only in selected regimes and limited changes in others.

BibTeX

@misc{FiklFildanKaslikMuresan_NODYCON_2026,
  title         = {Dynamics of Infinite Networks of Theta Neurons with Delays},
  author        = {Alexandru Fikl and Lavinia Fildan and Eva Kaslik and Raluca Mureșan},
  url           = {https://nodycon2026.app.earendelplatform.com/},
  eventdate     = {2026-09-23},
  eventtitle    = {Fifth International Nonlinear Dynamics Conference (NODYCON 2026)},
  venue         = {Sapienza University of Rome, Rome, Italy},
  type          = {Conference Presentation},
  language      = {en},
  abstract      = {
    We study an infinite all-to-all coupled network of identical theta neurons
    with synaptic interactions subject to distributed delays. Using the
    Watanabe–Strogatz transformation, linearization, and a characteristic
    equation expressed via the Laplace transform of the delay kernel, we
    analyze the local stability of equilibria and the effect of delays on
    macroscopic dynamics. We investigate whether different types of distributed
    delays may influence equilibrium stability and induce bifurcations.
    Numerical simulations support the analysis and reveal that delay effects on
    the global phase portrait are strongly parameter dependent, producing
    substantial qualitative changes only in selected regimes and limited
    changes in others.
  },
}