Bifurcation mechanism for emergence of spontaneous oscillations in coupled heterogeneous excitable units

Kai Morino, Gouhei Tanaka, Kazuyuki Aihara

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Biological systems are often composed of various heterogeneous excitable units. It is a fascinating problem to investigate how this heterogeneity affects collective behavior of biological systems. In this paper, to understand the effect of the unit heterogeneity on the dynamical mechanism for the onset of collective oscillatory behavior, we analyze coupled heterogeneous excitable units. We clarify how spontaneous oscillations emerge depending on the degree of heterogeneity of the units. With an increase in the coupling strength, the system undergoes a saddle-node on invariant circle bifurcation and a heteroclinic bifurcation. Based on bifurcation theory, we reveal that the order of the two bifurcations plays key roles in the mechanism of the emergence of spontaneous oscillations. In addition, we analytically show that when the system has a symmetric property, a 5th-order pitchfork bifurcation occurs instead of the two bifurcations. We also find that spontaneous oscillations are more likely to occur when the sizes of subpopulations of excitable units with different parameters are more balanced.

Original languageEnglish
Article number052210
JournalPhysical Review E
Volume98
Issue number5
DOIs
Publication statusPublished - Nov 9 2018
Externally publishedYes

Fingerprint

Bifurcation
Oscillation
oscillations
Unit
Biological Systems
saddles
Pitchfork Bifurcation
Collective Behavior
Bifurcation Theory
Saddle
Circle
Likely
Invariant
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Bifurcation mechanism for emergence of spontaneous oscillations in coupled heterogeneous excitable units. / Morino, Kai; Tanaka, Gouhei; Aihara, Kazuyuki.

In: Physical Review E, Vol. 98, No. 5, 052210, 09.11.2018.

Research output: Contribution to journalArticle

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