74 citations · 110 across the 11 of their papers we have counts for
12 papers
Analysing transitions from a Turing instability to large periodic patterns in a reaction-diffusion system
Christopher Brown, Gianne Derks, Peter van Heijster +1
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a t…
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,…
Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity
Jacob Brooks, Gianne Derks, David J. B. Lloyd
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corres…
A stability criterion for the non-linear wave equation with spatial inhomogeneity
Christopher J. K. Knight, Gianne Derks
In this paper the non-linear wave equation with a spatial inhomogeneity is considered. The inhomogeneity splits the unbounded spatial domain into three or more intervals, on each o…
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…
Pinned fluxons in a Josephson junction with a finite-length inhomogeneity
Gianne Derks, Arjen Doelman, Christopher J. K. Knight +1
We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon…