All Stories

  1. High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities

    Article • SIAM Journal on Applied Dynamical Systems, January 2021, Society for Industrial & Applied Mathematics (SIAM)

    Alejandro Rodríguez-Luis

  2. Asymptotic expansions for a family of non-generic canards using parametric representation

    Article • Applied Mathematics Letters, August 2020, Elsevier

    Alejandro Rodríguez-Luis

  3. Analytical approximation of cuspidal loops using a nonlinear time transformation method

    Article • Applied Mathematics and Computation, May 2020, Elsevier

    Alejandro Rodríguez-Luis

  4. Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method

    Article • Physica D Nonlinear Phenomena, May 2020, Elsevier

    Alejandro Rodríguez-Luis

  5. High-Order Analysis of Canard Explosion in the Brusselator Equations

    Article • International Journal of Bifurcation and Chaos, April 2020, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  6. High-order study of the canard explosion in an aircraft ground dynamics model

    Article • Nonlinear Dynamics, March 2020, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  7. Computation of all the coefficients for the global connections in theZ2-symmetric Takens-Bogdanov normal forms

    Article • Communications in Nonlinear Science and Numerical Simulation, February 2020, Elsevier

    Alejandro Rodríguez-Luis

  8. High-Order Analysis of Global Bifurcations in a Codimension-Three Takens–Bogdanov Singularity in Reversible Systems

    Article • International Journal of Bifurcation and Chaos, January 2020, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  9. Study of a simple 3D quadratic system with homoclinic flip bifurcations of inward twist case C

    Article • Communications in Nonlinear Science and Numerical Simulation, October 2019, Elsevier

    Alejandro Rodríguez-Luis

  10. A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens–Bogdanov normal form

    Article • Nonlinear Dynamics, June 2019, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  11. Revisiting the analysis of a codimension-three Takens–Bogdanov bifurcation in planar reversible systems

    Article • Nonlinear Dynamics, April 2019, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  12. Study of a dynamical system with a strange attractor and invariant tori

    Article • Physics Letters A, April 2019, Elsevier

    Alejandro Rodríguez-Luis

  13. Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D 4 symmetry

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, September 2018, American Institute of Physics

    Alejandro Rodríguez-Luis

  14. Comments on “Shilnikov chaos and Hopf bifurcation in three-dimensional differential system”

    Article • Optik, February 2018, Elsevier

    Alejandro Rodríguez-Luis

  15. A Review on Some Bifurcations in the Lorenz System

    Article • January 2018, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  16. Comments on “Asymptotically stable equilibrium points in new chaotic systems”

    Article • Nova Scientia, August 2017, Universidad de LaSalle Bajio

    Alejandro Rodríguez-Luis

  17. Superluminal periodic orbits in the Lorenz system

    Article • Communications in Nonlinear Science and Numerical Simulation, October 2016, Elsevier

    Alejandro Rodríguez-Luis

  18. Resonances of periodic orbits in the Lorenz system

    Article • Nonlinear Dynamics, February 2016, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  19. Takens–Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system

    Article • Communications in Nonlinear Science and Numerical Simulation, January 2016, Elsevier

    Alejandro Rodríguez-Luis

  20. Comment on “Study on the reliable computation time of the numerical model using the sliding temporal correlation method”

    Article • Theoretical and Applied Climatology, September 2015, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  21. An exact homoclinic orbit and its connection with the Rössler system

    Article • Physics Letters A, June 2015, Elsevier

    Alejandro Rodríguez-Luis

  22. Analysis of the T-point-Hopf bifurcation in the Lorenz system

    Article • Communications in Nonlinear Science and Numerical Simulation, May 2015, Elsevier

    Alejandro Rodríguez-Luis

  23. Comment on “Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems” [Appl. Math. Comput. 218 (2012) 11859–11870]

    Article • Applied Mathematics and Computation, October 2014, Elsevier

    Alejandro Rodríguez-Luis

  24. Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems

    Article • Nonlinear Dynamics, September 2014, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  25. Comments on “Invariant algebraic surfaces of the generalized Lorenz system”

    Article • Zeitschrift für angewandte Mathematik und Physik, April 2014, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  26. Centers on center manifolds in the Lorenz, Chen and Lü systems

    Article • Communications in Nonlinear Science and Numerical Simulation, April 2014, Elsevier

    Alejandro Rodríguez-Luis

  27. On Darboux polynomials and rational first integrals of the generalized Lorenz system

    Article • Bulletin des Sciences Mathématiques, April 2014, Elsevier

    Alejandro Rodríguez-Luis

  28. Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”, P. Yu, X.X. Liao, S.L. Xie, Y.L. Fu [Commun Nonlinear Sci Numer Simulat 14 (2009) 2886–2896]

    Article • Communications in Nonlinear Science and Numerical Simulation, March 2014, Elsevier

    Alejandro Rodríguez-Luis

  29. Comments on ‘Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces’

    Article • Physica D Nonlinear Phenomena, January 2014, Elsevier

    Alejandro Rodríguez-Luis

  30. Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang

    Article • Nonlinear Dynamics, November 2013, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  31. The Lü system is a particular case of the Lorenz system

    Article • Physics Letters A, November 2013, Elsevier

    Alejandro Rodríguez-Luis

  32. Comment on ‘Šilnikov-type orbits of Lorenz-family systems’ [Physica A 375 (2007) 438–446]

    Article • Physica A Statistical Mechanics and its Applications, October 2013, Elsevier

    Alejandro Rodríguez-Luis

  33. Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, September 2013, American Institute of Physics

    Alejandro Rodríguez-Luis

  34. Comment on ‘Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization’ [Chaos, Solitons and Fractals 44 (2011) 137–144]

    Article • Chaos Solitons & Fractals, September 2013, Elsevier

    Alejandro Rodríguez-Luis

  35. Comments on “Non-existence of Shilnikov chaos in continuous-time systems”

    Article • Applied Mathematics and Mechanics, July 2013, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  36. Comments on the paper “Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow”

    Article • Aerospace Science and Technology, July 2013, Elsevier

    Alejandro Rodríguez-Luis

  37. Comment on ‘Stability and chaos of a damped satellite partially filled with liquid’ [Acta Astronautica 65 (2009) 1628–1638]

    Article • Acta Astronautica, November 2012, Elsevier

    Alejandro Rodríguez-Luis

  38. Comments on “Analysis and application of a novel three-dimensional energy-saving and emission-reduction dynamic evolution system” [Energy 40 (2012) 291–299]

    Article • Energy, November 2012, Elsevier

    Alejandro Rodríguez-Luis

  39. Comment on “Existence of heteroclinic orbits of the Shilʼnikov type in a 3D quadratic autonomous chaotic system” [J. Math. Anal. Appl. 315 (2006) 106–119]

    Article • Journal of Mathematical Analysis and Applications, August 2012, Elsevier

    Alejandro Rodríguez-Luis

  40. On Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

    Article • Journal of Computational and Nonlinear Dynamics, July 2012, ASME International

    Alejandro Rodríguez-Luis

  41. Comment on “Heteroclinic orbits in Chen circuit with time delay” [Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 3058–3066]

    Article • Communications in Nonlinear Science and Numerical Simulation, June 2012, Elsevier

    Alejandro Rodríguez-Luis

  42. HOMOCLINIC INTERACTIONS NEAR A TRIPLE-ZERO DEGENERACY IN CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, June 2012, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  43. Rebuttal of “Existence of attractor and control of a 3D differential system” by Z. Wang

    Article • Nonlinear Dynamics, April 2012, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  44. Analysis of a Belyakov homoclinic connection with ℤ2-symmetry

    Article • Nonlinear Dynamics, December 2011, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  45. Comment on “Sil’nikov chaos of the Liu system” [Chaos 18, 013113 (2008)]

    Article • Chaos An Interdisciplinary Journal of Nonlinear Science, November 2011, American Institute of Physics

    Alejandro Rodríguez-Luis

  46. HOPF BIFURCATIONS AND THEIR DEGENERACIES IN CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, September 2011, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  47. Structure of saddle-node and cusp bifurcations of periodic orbits near a non-transversal T-point

    Article • Nonlinear Dynamics, September 2010, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  48. ANALYSIS OF THE T-POINT–HOPF BIFURCATION WITH ℤ2-SYMMETRY: APPLICATION TO CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, April 2010, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  49. Analysis of the T-point-Hopf bifurcation

    Article • Physica D Nonlinear Phenomena, March 2008, Elsevier

    Alejandro Rodríguez-Luis

  50. RESONANCES OF PERIODIC ORBITS IN RÖSSLER SYSTEM IN PRESENCE OF A TRIPLE-ZERO BIFURCATION

    Article • International Journal of Bifurcation and Chaos, June 2007, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  51. OPEN-TO-CLOSED CURVES OF SADDLE-NODE BIFURCATIONS OF PERIODIC ORBITS NEAR A NONTRANSVERSAL T-POINT IN CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, September 2006, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  52. HOMOCLINIC CONNECTIONS NEAR A BELYAKOV POINT IN CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, April 2005, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  53. A bifurcation analysis of a simple electronic circuit

    Article • Communications in Nonlinear Science and Numerical Simulation, March 2005, Elsevier

    Alejandro Rodríguez-Luis

  54. MULTIPARAMETRIC BIFURCATIONS IN AN ENZYME-CATALYZED REACTION MODEL

    Article • International Journal of Bifurcation and Chaos, March 2005, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  55. BI-SPIRALING HOMOCLINIC CURVES AROUND A T-POINT IN CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, May 2004, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  56. A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point

    Article • Physics Letters A, December 2003, Elsevier

    Alejandro Rodríguez-Luis

  57. CLOSED CURVES OF GLOBAL BIFURCATIONS IN CHUA'S EQUATION: A MECHANISM FOR THEIR FORMATION

    Article • International Journal of Bifurcation and Chaos, March 2003, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  58. SOME RESULTS ON CHUA'S EQUATION NEAR A TRIPLE-ZERO LINEAR DEGENERACY

    Article • International Journal of Bifurcation and Chaos, March 2003, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  59. A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING

    Article • International Journal of Bifurcation and Chaos, December 2002, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  60. Nontransversal curves of T-points: a source of closed curves of global bifurcations

    Article • Physics Letters A, October 2002, Elsevier

    Alejandro Rodríguez-Luis

  61. AN ANALYTICAL AND NUMERICAL STUDY OF A MODIFIED VAN DER POL OSCILLATOR

    Article • Journal of Sound and Vibration, September 2002, Elsevier

    Alejandro Rodríguez-Luis

  62. OSCILLATION-SLIDING IN A MODIFIED VAN DER POL–DUFFING ELECTRONIC OSCILLATOR

    Article • Journal of Sound and Vibration, January 2002, Elsevier

    Alejandro Rodríguez-Luis

  63. Article • Nonlinear Dynamics, January 2002, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  64. TAKENS–BOGDANOV BIFURCATIONS OF PERIODIC ORBITS AND ARNOLD'S TONGUES IN A THREE-DIMENSIONAL ELECTRONIC MODEL

    Article • International Journal of Bifurcation and Chaos, February 2001, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  65. ANALYTICAL PREDICTION OF THE TWO FIRST PERIOD-DOUBLINGS IN A THREE-DIMENSIONAL SYSTEM

    Article • International Journal of Bifurcation and Chaos, June 2000, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  66. ON THE HOPF–PITCHFORK BIFURCATION IN THE CHUA'S EQUATION

    Article • International Journal of Bifurcation and Chaos, February 2000, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  67. Article • Nonlinear Dynamics, January 2000, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  68. Article • Nonlinear Dynamics, January 2000, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  69. Article • Nonlinear Dynamics, January 2000, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  70. ON A CODIMENSION-THREE UNFOLDING OF THE INTERACTION OF DEGENERATE HOPF AND PITCHFORK BIFURCATIONS

    Article • International Journal of Bifurcation and Chaos, July 1999, World Scientific Pub Co Pte Lt

    Alejandro Rodríguez-Luis

  71. Analytical and numerical study of a four-parameter family of mechanical oscillators

    Article • Mechanics Research Communications, May 1999, Elsevier

    Alejandro Rodríguez-Luis

  72. The non-transverse Shil’nikov–Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies

    Article • Physica D Nonlinear Phenomena, April 1999, Elsevier

    Alejandro Rodríguez-Luis

  73. First-order approximation for canard periodic orbits in a van der Pol electronic oscillator

    Article • Applied Mathematics Letters, March 1999, Elsevier

    Alejandro Rodríguez-Luis

  74. Second period-doubling in a three-dimensional system

    Article • Mechanics Research Communications, March 1999, Elsevier

    Alejandro Rodríguez-Luis

  75. A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation

    Article • Nonlinearity, January 1999, Institute of Physics Publishing

    Alejandro Rodríguez-Luis

  76. Numerical continuation of degenerate homoclinic orbits in planar systems

    Article • IMA Journal of Numerical Analysis, January 1999, Oxford University Press (OUP)

    Alejandro Rodríguez-Luis

  77. Study of a degenerate bogdanov-takens bifurcation in a family of mechanical oscillators

    Article • Mechanics Research Communications, May 1998, Elsevier

    Alejandro Rodríguez-Luis

  78. Article • Nonlinear Dynamics, January 1998, Springer Science + Business Media

    Alejandro Rodríguez-Luis

  79. Isolas, cusps and global bifurcations in an electronic oscillator

    Article • Dynamics and Stability of Systems, January 1997, Taylor & Francis

    Alejandro Rodríguez-Luis

  80. A case study for homoclinic chaos in an autonomous electronic circuit

    Article • Physica D Nonlinear Phenomena, January 1993, Elsevier

    Alejandro Rodríguez-Luis

  81. Stationary instabilities in a dielectric liquid layer subjected to an arbitrary unipolar injection and an adverse thermal gradient

    Article • Journal of Physics D Applied Physics, November 1986, Institute of Physics Publishing

    Alejandro Rodríguez-Luis