22 citations · 50 across the 11 of their papers we have counts for
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Efficient Numerical Algorithms for Phase-Amplitude Reduction on the Slow Attracting Manifold of Limit cycles
David Reyner-Parra, Alberto Pérez-Cervera, Gemma Huguet
The phase-amplitude framework extends the classical phase reduction method by incorporating amplitude coordinates (or isostables) to describe transient dynamics transverse to the l…
Reconstruction of phase-amplitude dynamics from electrophysiological signals
Azamat Yeldesbay, Gemma Huguet, Silvia Daun
We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For thi…
Traveling waves in a model for cortical spreading depolarization with slow-fast dynamics
David Reyner-Parra, Carles Bonet, Teresa M. Seara +1
Cortical spreading depression and spreading depolarization (CSD) are waves of neuronal depolarization that spread across the cortex, leading to a temporary saturation of brain acti…
Global phase-amplitude description of oscillatory dynamics via the parameterization method
Alberto Pérez-Cervera, Tere M. Seara, Gemma Huguet
In this paper we use the parameterization method to provide a complete description of the dynamics of an -dimensional oscillator beyond the classical phase reduction. The parame…
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
A. Pérez-Cervera, P. Ashwin, G. Huguet +2
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter uncouples the system at . Using a normal form…
Quasi-periodic perturbations of heteroclinic attractor networks
Amadeu Delshams, Antoni Guillamon, Gemma Huguet
We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that Gamma distributions of dominance ti…
A geometric approach to Phase Response Curves and its numerical computation through the parameterization method
Alberto Pérez-Cervera, Tere M. Seara, Gemma Huguet
The Phase Response Curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the li…
Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models
Albert Granados, Gemma Huguet
In this work we consider a general class of -dimensional hybrid systems. Assuming that the system possesses an attracting equilibrium point, we show that, when periodically driv…
Fast iteration of cocyles over rotations and Computation of hyperbolic bundles
Gemma Huguet, Rafael de la Llave, Yannick Sire
In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of hyperbolic cocycles over a rotation. We present fast alg…
A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems
Amadeu Delshams, Gemma Huguet
In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in…
Computation of whiskered invariant tori and their associated manifolds: new fast algorithms
Gemma Huguet, Rafael de la Llave, Yannick Sire
In this paper we present efficient algorithms for the computation of several invariant objects for Hamiltonian dynamics. More precisely, we consider KAM tori (i.e diffeomorphic cop…