Travelling wave front solutions of a differential-difference equation arising in the modelling of myelinated nerve axon

1985 ◽  
pp. 77-89 ◽  
Author(s):  
N. F. Britton
Keyword(s):  
Difference Equation ◽  
Wave Front ◽  
Travelling Wave ◽  
Myelinated Nerve ◽  
Nerve Axon ◽  
Front Solutions ◽  
Differential Difference Equation ◽  
Travelling Wave Front

scholarly journals Thermally controlled glacier surging

2001 ◽  
Vol 47 (159) ◽  
pp. 527-538 ◽  
Author(s):  
A. C. Fowler ◽  
Tavi Murray ◽  
F. S. L. Ng
Keyword(s):  
Simple Model ◽  
Wave Front ◽  
Thermal Regime ◽  
Thick Layer ◽  
Travelling Wave ◽  
Yukon Territory ◽  
Wave Fronts ◽  
Ice Flow ◽  
Trapridge Glacier ◽  
Travelling Wave Front

AbstractBakaninbreen in Svalbard and Trapridge Glacier in Yukon Territory, Canada, are two prominent examples of surging glaciers which are thought to be controlled by their thermal regime. Both glaciers have developed large bulges which have propagated forward as travelling wave fronts, and which are thought to divide relatively stagnant downstream cold-based ice from faster-moving warm-based upstream ice. Additionally, both glaciers are underlain by a wet, metres thick layer of deforming till. We develop a simple model for the cyclic surging behaviour of these glaciers, which interrelates the motion of the ice and till through a description of the subglacial hydrology. We find that oscillations (surges) can occur if the subglacial hydrological transmissivity is sufficiently low and the till layer is sufficiently thin, and we suggest that these oscillations are associated with the development and propagation of a travelling wave front down the glacier. We therefore interpret the travelling wave fronts on both Trapridge Glacier and Bakaninbreen as manifestations of surges. In addition, we find that the violence of the surge in the model is associated with the resistance to ice flow offered by undulations in the bed, and the efficiency with which occasional hydrological events can release water accumulated at the glacier sole.

Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion

2004 ◽  
Vol 134 (3) ◽  
pp. 579-594 ◽  
Author(s):  
Ming Mei ◽  
Joseph W.-H. So ◽  
Michael Y. Li ◽  
Samuel S.P. Shen
Keyword(s):  
Asymptotic Stability ◽  
Wave Front ◽  
Nonlinear Stability ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Nicholson’S Blowflies Equation ◽  
Travelling Wave Front

This paper considers the nonlinear stability oftravelling wavefronts of a time-delayed diffusive Nicholson blowflies equation. We prove that, under a weighted L2 norm, ifa solution is sufficiently close to a travelling wave front initially, it converges exponentially to the wavefront as t → ∞. The rate ofconvergence is also estimated.

Existence and uniqueness of travelling waves for a neural network

1993 ◽  
Vol 123 (3) ◽  
pp. 461-478 ◽  
Author(s):  
G. Bard Ermentrout ◽  
J. Bryce McLeod
Keyword(s):  
Neural Network ◽  
Wave Front ◽  
Existence And Uniqueness ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Steady States ◽  
Stable States ◽  
One Dimensional ◽  
Travelling Wave Front

SynopsisA one-dimensional scalar neural network with two stable steady states is analysed. It is shown that there exists a unique monotone travelling wave front which joins the two stable states. Some additional properties of the wave such as the direction of its velocity are discussed.

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