Master Stability for Traveling Waves on Networks
Stefan Ruschel’s research focuses on dynamical systems theory and its applications to nonlinear optics and mathematical biology, among others. He specialises in analytical and numerical methods for delay differential and functional differential equations when the delay is large compared to other time scales of the system. His specific contributions include work on the fixed point spectrum for large delay, as well as the characterisation of slowly oscillating solutions such as travelling pulses and waves.
His future research is dedicated to applying these techniques to delay and lattice dynamical systems arising from coupled excitable and coupled bi-stable systems in laser dynamics and neuroscience, where such solutions play an important role in data transmission and neural signal propagation.
He is currently a research fellow at the University of Leeds (UK), funded by UKRI in recognition of a Horizon Europe MSCA award post-Brexit.
Abstract
I will present a new framework for determining effectively the spectrum and stability of traveling waves on networks with symmetries, such as rings and lattices, by computing master stability curves (MSCs). Unlike traditional methods, MSCs are independent of system size and can be readily used to assess wave destabilization and multi-stability in small and large networks.
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