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math.DS2026
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…
math.DS2021
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…
math.DS2019
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…