8 papers
On the initiation of spiral waves in excitable media
S. P. Hastings, M. M Sussman
Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medi…
Existence of Traveling Waves in a Neural Model
Stuart Hastings
In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of traveling wave fronts for a differential-integral equation modeling a neural network. Since then a number of…
An Elementary Approach to a Model Problem of Lagerstrom
S. P. Hastings, J. B. McLeod
The equation studied is u"+((n-1)/r)u'+epsilon u u'+ku'^{2}=0, with boundary conditions u(1)=0, u(infinity)=1. This model equation has been studied by many authors since it was int…
A congruence problem for polyhedra
Alexander Borisov, Mark Dickinson, Stuart Hastings
It is well known that to determine a triangle up to congruence requires three measurements: three sides, two sides and the included angle, or one side and two angles. We consider v…
A shooting approach to layers and chaos for a forced Duffing equation
SB. Ai, S. Hastings
We study equilibrium solutions for the problem ,. Using a shooting method we find solutions for all non-zero For small $ε…
On the global bifurcation diagram for the one-dimensional Ginzburg Landau model of superconductivity
E. N. Dancer, S. P. Hastings
Some new global results are given about solutions to the boundary value problem for the Euler-Lagrange equations for the Ginzburg-Landau model of a one-dimensional superconductor.…