Applied Mathematics

University of Zaragoza, Spain

Assistant Professor

Email: sserrano@unizar.es

Research fields

Numerical Analysis

Dynamical Systems

Qualifications

2003 Ph.D., Applied Mathematics, University of Zaragoza, Spain

1998 B.Sc., Applied Mathematics, University of Zaragoza, Spain

Publications (selected)

1. R. Barrio, M. Lefranc, M. A. Martínez, S. Serrano “Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models”, Europhysics Letters, 109 (2), 20002 (6pp.) (2015).
2. S. Serrano, R. Barrio, M. A. Martinez, A. Shilnikov “Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons”, Chaos, 24, 023128 (11 pp.) (2014).
3. F. Blesa, R. Barrio, S. Serrano “Unbounded dynamics in dissipative flows: Rössler model”, Chaos, 24, 024407 (13 pp.) (2014).
4. R. Barrio, H. Jiang, S. Serrano “A General Condition Number for Polynomials”, SIAM Journal on Numerical Analysis, 51 (2), 1280 - 1294, (2013).
5. R. Barrio, F. Blesa and S. Serrano “Topological Changes in Periodicity Hubs of Dissipative Systems”, Physical Review Letters, 108, 214102 (5 pp.) (2012).
6. R. Barrio, F. Blesa and S. Serrano “Behavior patterns in multiparametric dynamical systems: Lorenz model”, International Journal of Bifurcation and Chaos, 22, 1230019 (14 pp.) (2012).
7. A. Dena, M. Rodríguez, S. SerranoandR. Barrio, “High-Precision Continuation of Periodic Orbits”, Abstract and Applied Analysis, 2012, 716024 (12 pp.) (2012).
8. S. Serrano, R. Barrio, A. DenaandM. Rodríguez “Crisis curves in nonlinear business cycles”, Communications in Nonlinear Science and Numerical Simulation, 17, 788-794 (2012).
9. R. Barrio, F. Blesa, A. Dena and S. Serrano “Qualitative and numerical analysis of the Rössler model: Bifurcations of equilibria”, Computers and Mathematics with Applications, 62, 4140-4150 (2011).
10. R. Barrio, F. Blesa, S. Serrano andA. Shilnikov “Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci”, Physical Review E, 84, 035201 (5 pp.) (2011).
11. R. Barrio, M. Rodríguez, A. AbadandS. Serrano “Uncertainty propagation or box propagation”, Mathematical and Computer Modelling, 54, 2602-2615 (2011).
12. R. Barrio, F. BlesaandS. Serrano “Bifurcations and chaos in Hamiltonian systems”, International Journal of Bifurcation and Chaos, 20, 1293-1319 (2010).
13. S. Serrano “Asymptotic ordination of artificial satellite Hamiltonian”, Applied Mathematics and Computation, 215, 1124-1134 (2009).
14. R. Barrio andS. Serrano “Bounds for the chaotic region in the Lorenz model”, Physica D, 238, 1615-1624(2009).
15. R. Barrio, F. BlesaandS. Serrano “Bifurcations and safe regions in open Hamiltonians”, New Journal of Physics, 11 No 5, 053004 (15 pp) (2009).
16. R. Barrio, F. Blesaand S. Serrano “Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors”, Physica D, 238, 1087-1100, (2009).
17. R. Barrio, F. Blesaand S. Serrano “Periodic, escape and chaotic orbits in the Copenhagen and the (n+1)-body ring problems”, Communications in Nonlinear Science and Numerical Simulation 14, 2229-2238, (2009).
18. R. Barrio and S. Serrano “Performance of perturbation methods on orbit prediction”Mathematical and Computer Modelling, 48, n0. 3-4, 594-600, (2008).
19. R. Barrio, F. Blesaand S. Serrano "Qualitative analysis of the (N+1)-body ring problem” Chaos, Solitons&Fractals36, no.4, 1067-1088, (2008).
20. R. Barrio, F. Blesaand S. Serrano “Fractal Structures in the Hénon-Heiles Hamiltonian”Europhysics Letters, Vol. 82, no. 1, 10003 (6 pp) (2008).
21. R. Barrio and S. Serrano “A three-parametric study of the Lorenz model”Physica D 229, 43-51, (2007).
22. R. Barrio and S. Serrano "Modifications of the method of variation of parameteres” Computers and Mathematics with Applications, 51, no. 3-4, 451—466, (2006).
23. R. Barrio and S. Serrano "Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces II: numerical stability" Journal of Computational and Applied Mathematics 181, 299-320, (2005).
24. R. Barrio, B. Melendo andS. Serrano "Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces I: algorithms" Journal of Computational and Applied Mathematics 181, 280-298, (2005).
25. R. Barrio and S. Serrano "High order recurrences satisfied by classical orthogonal polynomials" Applied Mathematics Letters 17, 667-670, (2004).

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