151 citations · 740 across the 15 of their papers we have counts for
15 papers
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…
Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion
P. Parra-Rivas, D. Gomila, L. Gelens +1
We study the stability and bifurcation structure of spatially extended patterns arising in nonlin- ear optical resonators with a Kerr-type nonlinearity and anomalous group velocity…
Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
P. Parra-Rivas, D. Gomila, P. Colet +1
Bound states, also called soliton molecules, can form as a result of the interaction between individual solitons. This interaction is mediated through the tails of each soliton tha…
Front interaction induces excitable behavior
P. Parra-Rivas, M. A. Matias, P. Colet +3
Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitati…
Dark solitons in the Lugiato-Lefever equation with normal dispersion
Pedro Parra-Rivas, Edgar Knobloch, Damia Gomila +1
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organize…
Origin and stability of dark pulse Kerr combs in normal dispersion resonators
Pedro Parra-Rivas, Damia Gomila, Edgar Knobloch +2
We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato-Lefever model. We show that in the time domain these corres…
Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators
P. Parra-Rivas, D. Gomila, M. A. Matías +2
In Ref. [Parra-Rivas at al., 2013], using the Swift-Hohenberg equation, we introduced a mechanism that allows to generate oscillatory and excitable soliton dynamics. This mechanism…
Third-order chromatic dispersion stabilizes Kerr frequency combs
Pedro Parra-Rivas, Damia Gomila, Francois Leo +2
Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber…
Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs
P. Parra-Rivas, D. Gomila, M. A. Matias +2
It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we pre…
Dissipative soliton excitability induced by spatial inhomogeneities and drift
P. Parra-Rivas D. Gomila, M. A. Matias, P. Colet
We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, dissipative solitons in systems which do n…