Publications
Below my publications. In the section software you can find some of the routines that I have written to obtain the numerical demonstrations shown in some of these papers. Feel free to use them as you want; I would appreciate aknowledgement.Notes:
- the download process could take around 15 seconds to start, be patient...
- underlined authors the corresponding author.
Thesis
- [ PhD thesis ]: Local and global phenomena in piecewise-defined systems: from big bang bifurcations to splitting of heteroclinic manifolds Supervisors: Tere M.-Seara, Michael Schanz, 2012.
- [Master thesis]: Virtual orbits and two-parameter bifurcation analysis in power electronic converters. Supervisor: Enric Fossas, 2009.
- [ Final degree project (Master thesis, old system)] : Application of theory of averaging to power converters (in catalan). Supervisor: Enric Fossas, 2008.
Preprints and Monographs
-
The Scattering map in dissipative systems, applications to piezoelectric energy harvesters.
Albert Granados and Tere Seara , 2018.
[Preprint] -
Lecture notes: Notes on the computation of periodic orbits using Newton and Melnikov's method: Stroboscopic vs Poincaré map
, 2017.
[arXiv] -
Lecture notes: Apunts sobre curvatura 2n Batxillerat: concavitat i convexitat de funcions reals (in Catalan)
, 2006.
[pdf]
Peer-reviewed Journal publications
-
Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models
Albert Granados and Gemma Huguet
Communication in Nonlinear Science and Numerical Simulations 70, pp. 48-73, 2019.
DOI: doi.org/10.1016/j.cnsns.2018.09.006 or download the [pdf] -
Invariant manifolds and the parameterization method in coupled energy harvesting piezoelectric oscillators.
Albert Granados,
Physica D: Nonlinear Phenomena 351, pp. 14-29, 2017.
DOI: https://doi.org/10.1016/j.physd.2017.04.003 or download the [pdf]
[Preprint in arXiv]
See this animation. -
The period adding and incrementing bifurcations: from rotation theory to
applications
Albert Granados, LLuís Alsedà and Maciej Krupa
SIAM Review 59 Issue 2 pp. 225-292, 2017.
DOI: 10.1137/140996598 or download the [pdf] -
From canards of folded
singularities to torus canards in a forced van der Pol equation
J. Burke, Mathieu Desroches, Albert Granados, Tasso Kapper, Maciej Krupa and Theodore Vo.
Journal of Nonlinear Science, 26 pp. 405-451, 2016.
DOI: [dx.doi:10.1007/s00332-015-9279-0 or download the [pdf] -
Firing-rate, symbolic dynamics and frequency dependence in
periodically driven spiking models: a piecewise-smooth approach
Albert Granados and Maciej Krupa.
Nonliearity 28 pp. 1163-1192, 2015.
DOI: dx.doi:10.1088/0951-7715/28/5/1163 or download the [pdf] -
Border collision bifurcations of stroboscopic maps in periodically
driven spiking models
Albert Granados Maciej Krupa and Frédérique Clément.
SIAM Jour. Appl. Dyn. Syst. (SIADS), 13:4 pp. 1387-1416, 2014.
DOI: dx.doi.org/10.1137:13094637X or download the [pdf] -
The scattering map in two coupled piecewise-smooth systems, with
numerical application to rocking blocks
Albert Granados, John Hogan and Tere Seara
Physica D, 269 pp. 1-20, 2014, (published online Nov. 2013)
DOI: dx.doi.org/10.1016/j.physd.2013.11.008 or download the [pdf] -
Occurrence of big
bang bifurcations in discretized sliding-mode control systems
Enric Fossas and Albert Granados
Diff. Eqs. and Dyn. Syst. (DEDS), 21:1-2, pp.35-43, January 2013
DOI: dx.doi.org/10.1007/s12591-012-0121-y or download the [pdf] -
The Melnikov method and subharmonic
orbits in a piecewise-smooth system
Albert Granados, John Hogan and Tere Seara
SIAM Jour. Appl. Dyn. Syst. (SIADS) 11:3, pp.801-830, 2012
DOI: dx.doi.org/10.1137/110850359 or download the [pdf] -
Sufficient
conditions for a period incrementing big bang bifurcation in one-dimensional
maps
Viktor Avrutin, Albert Granados and Michael Schanz
Nonlinearity 24:9, pp. 2575-2598, 2011
DOI: dx.doi.org/10.1088/0951-7715/24/9/012 or download the [pdf] -
Virtual orbits and two-parameter bifurcation analysis in ZAD-controled
buck-converter
Viktor Avrutin, Enric Fossas, Albert Granados and Michael Schanz
Nonliniear Dynamics 63:1-2, pp. 19-33, 2011
DOI: dx.doi.org/10.1007/s11071-010-9782-7 or download the [pdf]
In proceedings
(not complete)-
Big bang bifurcations in a first order systems with a relay
Enric Fossas and Albert Granados
In proceedings the DSTA conference, Lodz, Poland, December 2011.
[pdf] -
Sufficient conditions for the period increment big bang bifurcation
in one dimensional non-smooth maps
Viktor Avrutin, Albert Granados and Michael Schanz
In proceedings of the XI International Conference Stability and Oscillations of Nonlinear Control Systems, 2010. -
Experimental procedure to obtain 2D time-space high-speed water surfaces.
A. Bateman, A. Granados, V. Medina, D. Velasco and M. Nalesso.
In proceedings of the International Conference of Fluvial Hydraulics, River Flow 2006, Lisbon, pp 1879 − 1888.
[pdf]