Entrainment dynamics of forced hierarchical circadian systems revealed by 2-dimensional maps

Document Type

Article

Publication Date

1-1-2020

Abstract

The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of its most important properties. A new tool, called the entrainment map, was recently introduced to study this process for a single oscillator. Here we generalize the map to study the effects of light-dark forcing in a hierarchical system consisting of a central circadian oscillator that drives a peripheral circadian oscillator. We develop techniques to reduce the higher-dimensional phase space of the coupled system to derive a generalized two-dimensional entrainment map. Determining the nature of various fixed points, together with an understanding of their stable and unstable manifolds, leads to conditions for existence and stability of periodic orbits of the circadian system. We use the map to investigate how various properties of solutions depend on parameters and initial conditions including the time to and direction of entrainment. We show that the concepts of phase advance and phase delay need to be carefully assessed when considering hierarchical systems.

Identifier

85091884280 (Scopus)

Publication Title

SIAM Journal on Applied Dynamical Systems

External Full Text Location

https://doi.org/10.1137/19M1307676

e-ISSN

15360040

First Page

2135

Last Page

2161

Issue

3

Volume

19

Grant

DMS-1555237

Fund Ref

National Science Foundation

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