Search

Skip to main content Accessibility help

Home
Search

Only show content I have access to (1)

Articles (1)

Over 3 years (1)

From year:

To year:

Apply

Mathematics (1)

92b25 biological rhythms and synchronisation

European Journal of Applied Mathematics (1)

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

1 results

Circle maps with gaps: Understanding the dynamics of the two-process model for sleep–wake regulation
M. P. BAILEY, G. DERKS, A. C. SKELDON
Journal:

European Journal of Applied Mathematics / Volume 29 / Issue 5 / October 2018

Published online by Cambridge University Press:

02 May 2018, pp. 845-868
- Article
- - You have access
- PDF
- Export citation
For more than 30 years the ‘two-process model’ has played a central role in the understanding of sleep/wake regulation. This ostensibly simple model is an interesting example of a non-smooth dynamical system, whose rich dynamical structure has been relatively unexplored. The two-process model can be framed as a one-dimensional map of the circle, which, for some parameter regimes, has gaps. We show how border collision bifurcations that arise naturally in maps with gaps extend and supplement the Arnold tongue saddle-node bifurcation set that is a feature of continuous circle maps. The novel picture that results shows how the periodic solutions that are created by saddle-node bifurcations in continuous maps transition to periodic solutions created by period-adding bifurcations as seen in maps with gaps.