Noise-induced phenomena in two strongly pulse-coupled spiking neurons

Kazuki Nakada, Keiji Miura, Hatsuo Hayashi

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


In this study, we address noise-induced phenomena in a system of two pulse-coupled resonate-and-fire neuron models as a piecewise smooth dynamical system. The model is a spiking neuron model that has second-order membrane dynamics with a firing threshold, and it exhibits subthreshold oscillation of membrane potential, resulting in the sensitivity to the timing of inputs. The pulse-coupled system shows the grazing bifurcation, a specific feature of a piecewise smooth dynamical system, as well as the saddle-node bifurcation. We numerically investigated mixture bifurcation structure of the system, leading to complex behaviors, such as burst synchronization and chaotic phenomena. Moreover, we found that a novel type of noise-induced order and chaos occur in the system when additive noise are given as a perturbation on the firing threshold. Finally, we will discuss a considerable mechanism of such noise-induced phenomena and the relationship to discontinuity-induced bifurcation in view of the piecewise smooth dynamical system theory.

Original languageEnglish
Pages (from-to)272-278
Number of pages7
JournalProcedia IUTAM
Publication statusPublished - 2012
EventIUTAM Symposium on 50 Years of Chaos: Applied and Theoretical - Kyoto, Japan
Duration: 2011 Nov 282011 Dec 2


  • Discontinuity-induced bifurcation
  • Noise-induced order and chaos
  • Piecewise smooth dynamical system
  • Pulse-coupled system
  • Resonate-and-fire neuron

ASJC Scopus subject areas

  • Mechanical Engineering


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