55 citations · 116 across the 7 of their papers we have counts for
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Spatial localization in the FitzHugh-Nagumo model
Pedro Parra-Rivas, Fahad Al Saadi, Lendert Gelens
The FitzHugh-Nagumo model, originally introduced to study neural dynamics, has since found applications across diverse fields, including cardiology and biology. However, the format…
Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines
Daniel Cebrián-Lacasa, Pedro Parra-Rivas, Daniel Ruiz-Reynés +1
The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicabi…
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…
Localized structures in dispersive and doubly resonant optical parametric oscillators
P. Parra-Rivas, L. Gelens, F. Leo
We study temporally localized structures in doubly resonant degenerate optical parametric oscillators in the absence of temporal walk-off. We focus on states formed through the loc…
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…
Observation of the Eckhaus Instability in Whispering-Gallery Mode Resonators
Damià Gomila, Pedro Parra-Rivas, Pere Colet +6
The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturb…