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Dynamic Games and Applications (2020) 10:79–99

https://doi.org/10.1007/s13235-019-00315-1

Jet Lag Recovery: Synchronization of Circadian Oscillators

as a Mean Field Game

René Carmona1·Christy V. Graves1

Published online: 25 May 2019

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Abstract

A mean ﬁeld game is proposed for the synchronization of oscillators facing conﬂicting

objectives. Our motivation is to offer an alternative to recent attempts to use dynamical

systems to illustrate some of the idiosyncrasies of jet lag recovery. Our analysis is driven

by two goals: (1) to understand the long time behavior of the oscillators when an individual

remains in the same time zone, and (2) to quantify the costs from jet lag recovery when

the individual has traveled across time zones. Finite difference schemes are used to ﬁnd

numerical approximations to the mean ﬁeld game solutions. They are benchmarked against

explicit solutions derived for a special case. Numerical results are presented and conjectures

are formulated. The numerics suggest that the cost the oscillators accrue while recovering is

larger for eastward travel which is consistent with the widely admitted wisdom that jet lag

is worse after traveling east than west.

Keywords Mean ﬁeld game ·Mean ﬁeld control ·Jet lag ·Synchronization ·Oscillators ·

Partial differential equations ·Explicit solutions ·Perturbation analysis ·Numerical results ·

Ergodic

1 Introduction

Circadian rhythm refers to the oscillatory behavior of certain biological processes occur-

ring with a period close to 24 h. Recent interest in these biological processes has spawned

from the Nobel Prize winning work of Hall, Rosbash, and Young, who discovered molecular

mechanisms for controlling the circadian rhythm in fruit ﬂies [20]. Examples of circadian

rhythms in animals include sleep/wake patterns, eating schedules, bodily temperatures, hor-

mone production, and brain activity. These oscillations can be entrained to the 24 h cycle of

Partially supported by NSF #DMS-1716673, ARO #W911NF-17-1-0578, and the NSF GRFP.

BChristy V. Graves

cjvaughn@princeton.edu

René Carmona

rcarmona@princeton.edu

1ORFE & PACM, Princeton University, Princeton, NJ 08544, USA

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