Sleep is important to all of us. Some of us – “larks” – perform best in the morning and thus make sure to go to bed early. For “owls” on the other hand, evening and night are the most important part of the day. Others fall in between these extremes or do not have regular sleep patterns at all. However, if we interact socially we influence each other’s daily rhythms and suddenly we end up going to bed a lot later than we normally would.
Recently, a huge study was performed at DTU in which 700 students were given smartphones that tracked over the course of several months when they turned on the screen, which other participants they called or texted (in an anonymized way), their location, etc. This rich dataset gives us hints about several aspects of the students’ lives, including sleep.
On the theoretical side, the emerging field of adaptive networks provides us with interesting differential equation systems. A typical model is the Kuramoto model with adaptive coupling.
In such networks, synchronization phenomena can be studied for one thing. Synchronization means – in our context – that different people go to bed at the same time, for example if they attended the same social gathering that evening, or they agreed to go running together each morning at a fixed time (and follow through).
Another aspect worth studying is the evolution of the coupling strengths between nodes in the network. If the coupling strength between student A and B increases, that means they start interacting more.
As always in dynamical systems, bifurcation and stability analysis is an important aspect too.
The aim of the project is to develop an adaptive network model of sleep synchronization that allows for the aforementioned analyses and explains the findings in the dataset.
Finally, adaptive networks can model many phenomena – also less creepy ones than sleep synchronization ;) – which is why we also aim to advance the understanding of these systems in general.