Inhibition-based relaxation oscillations emerge in resonator networks

Andrea Bel, Ana Torresi, Horacio G. Rotstein

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the mechanisms responsible for the generation of oscillations in mutually inhibitory cells of non-oscillatory neurons and the transitions from non-relaxation (sinusoidal-like) oscillations to relaxation oscillations. We use a minimal model consisting of a 2D linear resonator, a 1D linear cell and graded synaptic inhibition described by a piecewise linear sigmoidal function. Individually, resonators exhibit a peak in their response to oscillatory inputs at a preferred (resonant) frequency, but they do not show intrinsic (damped) oscillations in response to constant perturbations. We show that network oscillations emerge in this model for appropriate balance of the model parameters, particularly the connectivity strength and the steepness of the connectivity function. For fixed values of the latter, there is a transition from sinusoidal-like to relaxation oscillations as the connectivity strength increases. Similarly, for fixed connectivity strength values, increasing the connectivity steepness also leads to relaxation oscillations. Interestingly, relaxation oscillations are not observed when the 2D linear node is a damped oscillator. We discuss the role of the intrinsic properties of the participating nodes by focusing on the effect that the resonator’s resonant frequency has on the network frequency and amplitude.

Original languageEnglish (US)
Article number2019019
JournalMathematical Modelling of Natural Phenomena
Volume14
Issue number4
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • And phrases: Neural networks
  • Canard phenomenon
  • Relaxation oscillation
  • Resonance

Fingerprint

Dive into the research topics of 'Inhibition-based relaxation oscillations emerge in resonator networks'. Together they form a unique fingerprint.

Cite this