7 citations · 7 across the 1 of their papers we have counts for
5 papers
Bifurcation to instability through the lens of the Maslov index
Paul Cornwell, Christopher K. R. T. Jones, Claire Kiers
The Maslov index is a powerful tool for assessing the stability of solitary waves. Although it is difficult to calculate in general, a framework for doing so was recently establish…
Generalized Maslov indices for non-Hamiltonian systems
Thomas John Baird, Paul Cornwell, Graham Cox +2
We extend the definition of the Maslov index to a broad class of non-Hamiltonian dynamical systems. To do this, we introduce a family of topological spaces--which we call Maslov-Ar…
On the Existence and Stability of Fast Traveling Waves in a Doubly-Diffusive FitzHugh-Nagumo System
Paul Cornwell, Christopher K. R. T. Jones
The FitzHugh-Nagumo equation, which was derived as a simplification of the Hodgkin-Huxley model for nerve impulse propagation, has been extensively studied as a paradigmatic activa…
Opening the Maslov Box for Traveling Waves in Skew-Gradient Systems
Paul Cornwell
We obtain geometric insight into the stability of traveling pulses for reaction-diffusion equations with skew-gradient structure. For such systems, a Maslov index of the traveling…
A Stability Index for Traveling Waves in Activator-Inhibitor Systems
Paul Cornwell, Christopher K. R. T. Jones
We consider the stability of nonlinear traveling waves in a class of activator-inhibitor systems. The eigenvalue equation arising from linearizing about the wave is seen to preserv…