74 citations · 427 across the 35 of their papers we have counts for
27 papers · 1 filter
Nonuniform relaxation oscillations near SNIPER bifurcations
Edgar Knobloch, Arik Yochelis
Properties of spatially dependent relaxation oscillations near a SNIPER bifurcation are described. A SNIPER bifurcation creates a large-amplitude long-period periodic orbit via the…
Localized spatiotemporal reaction-diffusion patterns on a line and a disk arising from a subcritical finite wavenumber Hopf instability
Edgar Knobloch, Saar O. Modai, Hannes Uecker +1
Spatiotemporal localized and extended structures associated with a subcritical finite wavenumber Hopf bifurcation are studied in the Purwins model (a three-variable FitzHugh-Nagumo…
A mass conserved reaction-diffusion system reveals switching between coexisting polar and oscillatory cell motility states
Jack M. Hughes, Cristina Martinez-Torres, Carsten Beta +2
Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes…
Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves
Jack M. Hughes, Saar Modai, Leah Edelstein-Keshet +1
Eukaryotic cells demonstrate a wide variety of dynamic patterns of filamentous actin (F-actin) and its regulators. Some of these patterns play important roles in cell functions, su…
Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics
Edgar Knobloch, Arik Yochelis
Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence…
Front propagation and global bifurcations in a multivariable reaction-diffusion model
Edgar Knobloch, Arik Yochelis
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-in…