74 citations · 201 across the 6 of their papers we have counts for
7 papers
Creation of discontinuities in circle maps
Gianne Derks, Paul A. Glendinning, Anne C. Skeldon
Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and `threshold' systems such as integrate and fire neuronal models,…
Can weakly nonlinear theory explain Faraday wave patterns near onset?
A. C. Skeldon, A. M. Rucklidge
The Faraday problem is an important pattern-forming system that provides some middle ground between systems where the initial instability involves just a single mode and in which c…
Mathematical models for sleep-wake dynamics: comparison of the two-process model and a mutual inhibition neuronal model
Anne C. Skeldon, Derk-Jan Dijk, Gianne Derks
Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing propose…
Three-wave interactions and spatio-temporal chaos
Alastair M. Rucklidge, Mary Silber, Anne C. Skeldon
Three-wave interactions form the basis of our understanding of many pattern forming systems because they encapsulate the most basic nonlinear interactions. In problems with two com…
Two-frequency forced Faraday waves: Weakly damped modes and pattern selection
Mary Silber, Chad M. Topaz, Anne C. Skeldon
Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency parametrically excited surface waves exhibit an intriguing "superlattice" wave pattern near a codimension-two…
New stability results for long-wavelength convection patterns
Anne C. Skeldon, Mary Silber
We consider the transition from a spatially uniform state to a steady, spatially-periodic pattern in a partial differential equation describing long-wavelength convection. This bot…