79 citations · 79 across the 6 of their papers we have counts for
6 papers
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…
Time-dependent localized patterns in a predator-prey model
Fahad Al Saadi, Edgar Knobloch, Mark Nelson +1
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two re…
Organization of spatially localized structures near a codimension-three cusp-Turing bifurcation
P. Parra-Rivas, A. R. Champneys, F. Al-Sahadi +2
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial…
Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities
P. Parra-Rivas, E. Knobloch, L. Gelens +1
Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, w…
Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion
P. Parra-Rivas, D. Gomila, L. Gelens +1
The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is studied. This mean field model descri…