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Jet Lag Recovery: Synchronization of Circadian Oscillators as a Mean Field Game

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Rene A. Carmona at Princeton University
Rene A. Carmona
Christy V. Graves
Christy V. Graves
Christy V. Graves
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Abstract and Figures

The Suprachiasmatic Nucleus (SCN) is a region in the brain that is responsible for controlling circadian rhythms. The SCN contains on the order of 10^4 neuronal oscillators which have a preferred period slightly longer than 24 hours. The oscillators try to synchronize with each other as well as responding to external stimuli such as sunlight exposure. A mean field game model for these neuronal oscillators is formulated with two goals in mind: 1) to understand the long time behavior of the oscillators when an individual remains in the same time zone, and 2) to understand how the oscillators recover from jet lag when the individual has traveled across time zones. In particular, we would like to study the claim that jet lag is worse after traveling east than west. Finite difference schemes are used to find numerical approximations to the mean field game solutions. Numerical results are presented and conjectures are posed. The numerics suggest the time to recover from jet lag is about the same for east versus west trips, but the cost the oscillators accrue while recovering is larger for eastward trips.
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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
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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