The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems
Document Type
Article
Publication Date
6-1-2022
Abstract
Several distinct entrainment patterns can occur in the FitzHugh-Nagumo (FHN) model under external periodic forcing. Investigating the FHN model under different types of periodic forcing reveals the existence of multiple disconnected 1:1 entrainment segments for constant, low enough values of the input amplitude when the unforced system is in the vicinity of a Hopf bifurcation. This entrainment structure is termed polyglot to distinguish it from the single 1:1 entrainment region (monoglot) structure typically observed in Arnold tongue diagrams. The emergence of polyglot entrainment is then explained using phase-plane analysis and other dynamical system tools. Entrainment results are investigated for other slow-fast systems of neuronal, circadian, and glycolytic oscillations. Exploring these models, we found that polyglot entrainment structure (multiple 1:1 regions) is observed when the unforced system is in the vicinity of a Hopf bifurcation and the Hopf point is located near a knee of a cubic-like nullcline.
Identifier
85133822742 (Scopus)
Publication Title
Chaos
External Full Text Location
https://doi.org/10.1063/5.0079198
e-ISSN
10897682
ISSN
10541500
PubMed ID
35778129
Issue
6
Volume
32
Grant
1313861
Fund Ref
National Science Foundation
Recommended Citation
Khan, Emel; Saghafi, Soheil; Diekman, Casey O.; and Rotstein, Horacio G., "The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems" (2022). Faculty Publications. 2913.
https://digitalcommons.njit.edu/fac_pubs/2913