Sistemas LPP (PWL)

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Compartimos referencias relacionadas directa o indirectamente con sistemas dinámicos modelados mediante sistemas de ecuaciones diferenciales definidos por tramos (en ingl. se incluye p. ej. PSS, PWL, PWA Systems). Se indican también algunas referencias contextuales. 

[Rev. 2017.04.22]


  1. ∃Alzate Castaño, Ricardo (2008) Analysis and application of bifurcations in systems with impact and chattering. PhD Dissertation.{Tutor: Prof. Mario di Bernardo}  [acc. 2014.12.25]
  2. Barton, David A. W. (2009) Stability calculations for piecewise-smooth delay equations, International Journal of Bifurcation and Chaos, vol 19., pp. 639-650 [acc. 2014.01.08]
  3. Benmerzouk, Djamila & Jean-Pierre Barbot.(2009)Chaotification of piecewise smooth systems. Chaos 09, Londre, United Kingdom. <hal-00772236> [acc. 2014.12.25]
  4. τBiemond, J. J. B. et al. (2009) A complete bifurcation analysis of planar conewise affine systems. [acc. 2014.10.12]
  5. τBiemond, J. J. B. et al. (2010) Nonsmooth bifurcations of equilibria in planar continuous systems. Nonlinear Analysis: Hibrid systems 4, 451-474. Elsevier {∃see procedure in section 4.3} [acc. 2014.09.15]
  6. Brandon, Quentin (2009) →Numerical Method of Bifurcation Analysis for Piecewise-smooth Nonlinear Dynamical Systems. Tesis Doctoral {ver también: ⇒Numerical Method of Bifurcation Analysis for Piecewise-smooth Nonlinear Dynamical Systems: Application to Alpazur oscillator}[acc. 2014.01.08]
  7. Broucke, Mireille E. et al. (2001) Structural stability of piecewise smooth systems. [acc. 2014.01.08]
  8. Burden, Samuel A. et al. (2013) Model reduction near periodic orbits of hybrid dynamical systems. [acc. 2015.01.16]
  9. ℵBurden, Samuel A. et al. (2014) Event–Selected Vector Field Discontinuities Yield Piecewise–Differentiable Flows. [acc. 2014.12.25]
  10. τℵCarmona Centeno, Victoriano (2002) Bifurcaciones en sistemas dinámicos lineales a trozos. Tesis doctoral. Univ. de Sevilla, España [2015.04.21]
  11. ∃Champnewys, Alan R, Mario di Bernardo (2008) Piecewise smooth dynamical systems. Scholarpedia 3(9):4041  [acc, 2014.12.25]
  12. ∀Champneys, Alan (2009) Rock, Rattle and Slide bifurcation theory for piecewise-smooth systems. [acc. 2014.12.25]
  13. Colombo, A. et al. (2009) Stable Manifolds of Saddles in Piecewise Smooth Systems. CMES, vol.53, no.3, pp.235-254 [acc. 2014.01.08]
  14. Colombo, A. et al. (2010) ♦Teixeira singularities in 3D switched feedback control systems. Systems & Control Letters, 59 (10). pp. 615-622 [acc. 2014.01.08]
  15. Colombo, A. et al. (2012) ♦Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems. Physica D 241 (2012) 1845–1860 Elsevier [acc. 2014.01.08]
  16. Dercole, Fabio, et al. (2007) Bifurcation analysis of piecewise smooth ecological models. Theoretical Population Biology 72 (2007) 197–213 [acc. 2014.10.31]
  17. di Bernardo, Mario et al. (2000) Unified derivation of normal form maps for grazing bifurcations in n-dimensional piecewise dynamical systems. [acc. 2015.01.16]
  18. di Bernardo, Mario (2008) Discontinuity-induced Bifurcations of Equilibria in piecewise-smooth systems.CDS08 Monopoli [acc. 2014.12.25]
  19. di Bernardo, Mario (2008) Discontinuity-induced Bifurcations of Limit Cycles in piecewise-smooth systems.CDS08 Monopoli [acc. 2014.01.09]
  20. di Bernardo, Mario et al. (2008) Bifurcations in Nonsmooth Dynamical Systems. SIAM Reviews Vol. 50, No. 4, pp. 629–701. [acc. 2014.01.08]
  21. ∃di Bernardo, Mario & S. J. Hogan (2010) Discontinuity-induced bifurcations of piecewise smooth dynamical systems. Phil. Trans. R. Soc. A (2010) 368, 4915–4935 [acc. 2014.12.25]
  22. di Bernardo, Mario (2011) ⇒Adaptive Control and Synchronization of PWS systems and networks. ISCDE, Batz-sur-Mer. [acc. 2014.10.31]
  23. ∀Dieci, Luca & Luciano Lopez (2009) →Fundamental matrix solutions of piecewise smooth differential systems. {Draft} {ver también: Mathematics and Computers in Simulation 81 (2011) 932–953 ⇒ScienceDirect MATCOM paper, (contiene link a PDF)} [acc. 2014.01.08]
  24. Doedel, Eusebius (2010) →Lecture Notes on Numerical Analysis of Nonlinear Equations. [acc. 2014.01.08]
  25. Elmegårt, M. et al. (2013) Bifurcation analysis of a smoothed model of a forced impacting beam and comparison with an experiment. Arxiv [acc. 2014.01.08]
  26. ℵτFernandez-García, Soledad (2012) Bifurcaciones de Órbitas Periódicas y Conjuntos Invariantes en Sistemas Dinámicos Lineales a Trozos. Tesis Doctoral, Univ. de Sevilla [acc. 2015.04.10]
  27. Ferrer, J. et al. (2011) Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization.
    Preprint [acc. 2017.04.22]
  28. Ferrer, J. et al. (2013) Structural Stability of Planar Bimodal Linear Systems.
    11th International Conference of Numerical Analysis and Applied Mathematics 2013 AIP Conf. Proc. 1558, 2205-2208  [acc. 2017.04.22]
  29. λGalias, Z. (2011) On rigorous integration of piece-wise linear systems. [acc. 2014.11.18]
  30. ℵτGarcía-Medina, Elisabeth (2012) Conexiones Globales y Comportamientos Periódicos en Sistemas Dinámicos Lineales a Trozos. Tesis Doctoral. Univ. de Sevilla [acc. 2015.04.10]
  31. ℵτGarcía-Medina, Elisabeth (2012) “Existence of global connections in three-dimensional piecewise linear systems“. [acc. 2015.03.23]
  32. Gardini, Laura & Fabio Tramontana (2012) Structurally unstable regular dynamics in 1D piecewise smooth maps, and circle maps. Chaos, Solitons & Fractals 45 (2012) 1328–1342, Elsevier [acc. 2014.01.08]
  33. τGranados, A et al. (2012) The Melnikov method and subharmonic orbits in a piecewise smooth system. Arxiv. [acc. 2014.09.15]
  34. ∑τGranados, A et al. (2012) Local and global phenomena in piecewise-defined systems: from big bang bifurcations to splitting of heteroclinic manifolds. {Tesis} [acc. 2014.10.12]
  35. Hogan, John (2012) ∑Piecewise smooth dynamical systems. Dynamical Systems: 100 years after Poincaré. Gijón, Spain [acc. 2014.01.10]
  36. τ²Ivanov, Alexander P. (2012) Analysis of discountinuous bifurcations in nonsmooth dynamical systems. [acc. 2015.01.21]
  37. Jacquemard, Alain et al. (2012) Stability conditions in piecewise smooth dynamical systems at a two-fold singularity. [acc. 2014.01.08]
  38. Jeffrey, M. R & A. Colombo (2009) The Two-Fold Singularity of Discontinuous Vector Fields. SIAM J. Applied Dynamical Systems, Vol. 8, No. 2, pp. 624–640  [acc. 2014.01.09]
  39. λKersing, Stefan & Martin Buss (2014) Adaptive identification of continuous-time switched linear and piecewise linear systems. [acc. 2014.11.18]
  40. Kristiansen, K. U. & J. Hogan (2014) On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems en  R^3.  [acc. 2014.11.30]
  41. ℵKuznetson, Yu A. (2000) Lecture Notes of Numerical Bifurcation Analysis: [acc. 2014.12.13]
    1. [L1] ⇒Continuation problems. Numerical continuation of equilibria and limit cycles of ODEs.
    2. [L2] ⇒Equilibrium bifurcations of ODEs and their numerical analysis.
    3. [L3] ⇒Bifurcations of limit cycles of ODEs and their numerical analysis using BVPs.
    4. [L4] ⇒Numerical local bifurcation analysis of iterated maps.
    5. [L5] Numerical continuation of connecting orbits of iterated maps and ODEs.
  42. Kuznetsov, Yu A. et al. (2003) ♦One-parameter bifurcations in planar Filippov systems. International Journal of Bifurcation and Chaos, Vol. 13, No. 8 (2003) 2157-2188 [acc. 2014.01.08]
  43. Leine, R. I. (2006) Bifurcations of equilibria in non-smooth continuous systems. Physica D 223 (2006) 121–137 [acc. 2014.01.09]
  44. ℵτLlibre, Jaime; Ponce, Enrique; Torres, Francisco (2009) Dos bifurcaciones de ciclos límite en sistemas lineales a trozos en  R^3. [acc. 2015.04.10]
  45. ∏τMezic, I., Stephen Wiggins (1999) A method for visualization of invariant sets of dynamical systems based on the ergodic partition. Chaos 9:1 [acc. 2014.10.12]
  46. τPonce, E. (2012) Piecewise Linear Systems: twenty years on. [acc. 2015.04.09]
  47. τPonce, E. (2014) Bifurcations in piecewise linear systems: case studies. MAT70 An international conference on dynamical systems in honor of the 70th birthday of Marco Antonio Texeira. Notes of a Mini-course held at IMECC, Campinas, São Paulo. [acc, 2014.10.12]
  48. Russo, Giovanni & Marco di Bernardo (2011) On Contraction of Piecewise Smooth Dynamical Systems. Preprints of the 18th IFAC World Congress Milano (Italy) August 28 – September 2, 2011 [acc. 2014.01.08]
  49. Salinas-Varela, Adrián A. et al. (2009)Analysis of piecewise linear (PWL) feedback systems. [acc. 2014.11.18]
  50. Sieber, J. & P. Kowalczyk (2010) Small-scale instabilities in dynamical systems with sliding. Arxiv. [acc. 2014.01.09]
  51. Simpson, D. J. W. & R. Kuske (2012) Stochastically Perturbed Sliding Motion in Piecewise-Smooth Systems. Arxiv [acc. 2014.01.09]
  52. ℵSimpson, D.J.W. & J. D. Meiss (2007) Andronov–Hopf bifurcations in planar, piecewise-smooth, continuous flows [acc. 2014.12.23]
  53. ℵSimpson, D.J.W. & J. D. Meiss (2010) Aspects of  Bifurcation Theory for Piecewise-Smooth, Continuous Systems [acc. 2014.12.23]
  54. ℵSvahn, Fredrik (2009) On the stability and control of piecewise-smooth dynamical systems with impacts and friction. Doctoral Thesis. [acc. 2014.01.08]
  55. ℵSzalai, Róbert, et al. (2008) Arnold’s tongues arising from a grazing-sliding bifurcation of a piecewise-smooth system. [acc. 2014.12.25]
  56. ∑τWarwick, D. J. (2010) Fundamentals of Piecewise-Smooth Continuous Systems. {Book chapter} [acc. 2014.10.12]
  57. ℵXu, Bin et al. (2013) Homoclinic bifurcations in planar piecewise-linear systems. Discrete Dynamics in Nature and Society, Vol. 2013 [acc. 2014.12.23]
  58. Yang, Xiao-Song et al. (c. 2008) Existence and bifurcation of homoclinic orbits in planar piecewise linear systems. Arxiv [acc. 2014.01.08]



  1. Applied Nonlinear Mathematics. University of Bristol
  2. Dance-Net. Coordinadores Lluís Alsedà (UAB) y Enrique Ponce (US)



  1. AUTO
  2. [Comercial] Phaser: a universal simulator for dynamical systems
  3. τDe Witte, V et al. (2012) Interactive initialization and continuation of homoclinic and heteroclinic orbits in Matlab. ACM Transactions of Mathematical Software 38 (3) art. 18 [acc. 2014.09.15]


Normal Forms (selected)

Moduli spaces connection

Libros selectos (de libre acceso)