16 citations · 46 across the 9 of their papers we have counts for
10 papers · 1 filter
Arnold diffusion for an a priori unstable Hamiltonian system with 3 1/2 degrees of freedom
Amadeu Delshams, Albert Granados, Rodrigo G. Schaefer
In the present paper we apply the geometrical mechanism of diffusion in an \emph{a priori} unstable Hamiltonian system with 3 1/2 degrees of freedom. This mechanism consists of…
Notes on the computation of periodic orbits using Newton and Melnikov's method
Albert Granados
These notes were written during the 9th and 10th sessions of the subject Dynamical Systems II coursed at DTU (Denmark) during the Winter Semester 2015-2016, and later extended in F…
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…
Invariant manifolds and the parameterization method in coupled energy harvesting piezoelectric oscillators
Albert Granados
Energy harvesting systems based on oscillators aim to capture energy from mechanical oscillations and convert it into electrical energy. Widely extended are those based on piezoele…
From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation
J. Burke, M. Desroches, A. Granados +3
We study canard solutions of the forced van der Pol (fvdP) equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observ…
The Period adding and incrementing bifurcations: from rotation theory to applications
Albert Granados, Lluís Alsedà, Martin Krupa
This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through t…
Border collision bifurcations of stroboscopic maps in periodically driven spiking models
Albert Granados, Martin Krupa, Frédérique Clément
In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excit…
Firing-rate, symbolic dynamics and frequency dependence in periodically driven spiking models: a piecewise-smooth approach
Albert Granados, Maciej Krupa
In this work we consider a periodically forced generic integrate-and-fire model with a unique attracting equilibrium in the subthreshold dynamics and study the dependence of the fi…
The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
A. Granados, S. J. Hogan, T. M. Seara
We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in $\RR^2$ through a non-autonomous periodic perturbation. We study the dynamics aroun…
The Melnikov method and subharmonic orbits in a piecewise smooth system
A. Granados, S. J. Hogan, T. M. Seara
In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold . We assume that there exists a piecewise-define…