4 papers
Kernel-Dependent Pattern Formation in a Population Model with Nonlocal Facilitation and Competition
Olivia Clifton, Stephanie Dodson, Daniel B. Cooney
Spatial patterns, such as those in dryland vegetation models, have historically been studied in systems of reaction-diffusion systems with pattern onset via a Turing bifurcation fr…
Efficient numerical computation of spiral spectra with exponentially-weighted preconditioners
Stephanie Dodson, Ryan Goh, Bjorn Sandstede
The stability of nonlinear waves on spatially extended domains is commonly probed by computing the spectrum of the linearization of the underlying PDE about the wave profile. It is…
Reflections in excitable media linked to existence and stability of one-dimensional spiral waves
Stephanie Dodson, Timothy J. Lewis
When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with t…
Determining the source of period-doubling instabilities in spiral waves
Stephanie Dodson, Bjorn Sandstede
Spiral wave patterns observed in models of cardiac arrhythmias and chemical oscillations develop alternans and stationary line defects, which can both be thought of as period-doubl…