$$ \newcommand{\R}{\mathbb{R}} \newcommand{\RR}{\mathbb{R}} \newcommand{\Nuc}{\text{Nuc}} %\newcommand{\vv}[1]{\overrightarrow{#1}} \newcommand{\vv}[1]{\vec{#1}} \newcommand{\D}{\text{Dom}} \newcommand{\Dom}{\text{Dom}} $$

Publicacions

A continuació teniu un llistat de les meves publicacions. A la secció de Programari podeu trobar algunes de les rutines que he escrit per obtenir les demostracions numèriques que es mostren en alguns d’aquests articles. Sou lliures d’utilitzar-les; agrairia menció/reconeixement si ho feu.

Notes:

• Els autors subratllats o en negreta indiquen l’autor de correspondència.

Tesis

• [ 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.

• [ Tesis Final de Master ]: Virtual orbits and two-parameter bifurcation analysis in power electronic converters Supervisor: Enric Fossas, 2009.

• [ Projecte final de carrera ]: Application of theory of averaging to power converters (en català) Supervisor: Enric Fossas, 2008.

Preprints i Monografies

• The Scattering map in dissipative systems, applications to piezoelectric energy harvesters. Albert Granados i 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]

• Apunts docents: Apunts sobre curvatura 2n Batxillerat: concavitat i convexitat de funcions reals, 2006. [pdf]

Articles en revistes (Peer-reviewed)

• Arnold diffusion for an a priori unstable Hamiltonian system with 3+1/2 degrees of freedom Albert Granados, Amadeu Delshams i Rodrigo Gonzalves Schaefer Chaos 34, 2024. DOI: 10.1063/5.0185044

• Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models Albert Granados i Gemma Huguet Communication in Nonlinear Science and Numerical Simulations 70, pp. 48-73, 2019. DOI: 10.1016/j.cnsns.2018.09.006 o descarrega el [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: 10.1016/j.physd.2017.04.003 o descarrega el [pdf] (Veure també Preprint a arXiv i aquesta animació)

• The period adding and incrementing bifurcations: from rotation theory to applications Albert Granados, LLuís Alsedà i Maciej Krupa SIAM Review 59 Issue 2 pp. 225-292, 2017. DOI: 10.1137/140996598 o descarrega el [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 i Theodore Vo. Journal of Nonlinear Science, 26 pp. 405-451, 2016. DOI: 10.1007/s00332-015-9279-0 o descarrega el [pdf]

• Firing-rate, symbolic dynamics and frequency dependence in periodically driven spiking models: a piecewise-smooth approach Albert Granados i Maciej Krupa. Nonlinearity 28 pp. 1163-1192, 2015. DOI: 10.1088/0951-7715/28/5/1163 o descarrega el [pdf]

• Border collision bifurcations of stroboscopic maps in periodically driven spiking models Albert Granados, Maciej Krupa i Frédérique Clément. SIAM Jour. Appl. Dyn. Syst. (SIADS), 13:4 pp. 1387-1416, 2014. DOI: 10.1137/13094637X o descarrega el [pdf]

• The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks Albert Granados, John Hogan i Tere Seara Physica D, 269 pp. 1-20, 2014. DOI: 10.1016/j.physd.2013.11.008 o descarrega el [pdf]

• Occurrence of big bang bifurcations in discretized sliding-mode control systems Enric Fossas i Albert Granados Diff. Eqs. and Dyn. Syst. (DEDS), 21:1-2, pp.35-43, 2013. DOI: 10.1007/s12591-012-0121-y o descarrega el [pdf]

• The Melnikov method and subharmonic orbits in a piecewise-smooth system Albert Granados, John Hogan i Tere Seara SIAM Jour. Appl. Dyn. Syst. (SIADS) 11:3, pp.801-830, 2012. DOI: 10.1137/110850359 o descarrega el [pdf]

• Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps Viktor Avrutin, Albert Granados i Michael Schanz. Nonlinearity 24:9, pp. 2575-2598, 2011. DOI: 10.1088/0951-7715/24/9/012 o descarrega el [pdf]

• Virtual orbits and two-parameter bifurcation analysis in ZAD-controled buck-converter Viktor Avrutin, Enric Fossas, Albert Granados i Michael Schanz. Nonlinear Dynamics 63:1-2, pp. 19-33, 2011. DOI: 10.1007/s11071-010-9782-7 o descarrega el [pdf]

Actes de congressos (Proceedings)

• Big bang bifurcations in a first order systems with a relay Enric Fossas i Albert Granados In proceedings of 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 i 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 i M. Nalesso. In proceedings of the International Conference of Fluvial Hydraulics, River Flow 2006, Lisbon, pp 1879 − 1888. [pdf]