Edit Profile (opens in new tab) Rodríguez-Luis, Alejandro J. Co-Author Distance Author ID: rodriguez-luis.alejandro-j Published as: Rodríguez-Luis, A. J.; Rodríguez-Luis, Alejandro J.; Rodríguez Luis, Alejandro J.; Rodríguez Luis, A. J. more...less Documents Indexed: 81 Publications since 1989 Co-Authors: 15 Co-Authors with 81 Joint Publications 328 Co-Co-Authors all top 5 Co-Authors 0 single-authored 55 Algaba, Antonio 37 Freire Macías, Emilio 33 Merino, Manuel 29 Fernández-Sánchez, Fernando 21 Gamero, Estanislao 13 Qin, Bo-Wei 12 Chung, Kwok-Wai 7 Pizarro, Luis 4 Domínguez-Moreno, María C. 3 Belhaq, Mohamed 3 Ponce, Enrique 2 Houssni, Mohamed 2 Ponce Núñez, Enrique 1 Champneys, Alan R. 1 Doedel, Eusebius J. all top 5 Serials 16 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Nonlinear Dynamics 9 Communications in Nonlinear Science and Numerical Simulation 6 Physica D 5 Physics Letters. A 3 Applied Mathematics Letters 3 Chaos 2 Journal of Sound and Vibration 2 Applied Mathematics and Computation 2 Dynamics and Stability of Systems 1 IMA Journal of Numerical Analysis 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Physica A 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Chaos, Solitons and Fractals 1 Mechanics Research Communications 1 Applied Mathematics and Mechanics. (English Edition) 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Bulletin des Sciences Mathématiques 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 SIAM Journal on Applied Dynamical Systems all top 5 Fields 61 Ordinary differential equations (34-XX) 50 Dynamical systems and ergodic theory (37-XX) 10 Mechanics of particles and systems (70-XX) 5 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Information and communication theory, circuits (94-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 70 Publications have been cited 585 times in 259 Documents Cited by ▼ Year ▼ A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. Zbl 1043.37042 Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A. 34 2002 Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system. Zbl 1323.37020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 32 2013 A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Sil’nikov. Zbl 0809.58040 Freire, E.; Rodríguez-Luis, A. J.; Gamero, E.; Ponce, E. 26 1993 The Lü system is a particular case of the Lorenz system. Zbl 1301.37020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 24 2013 Some results on Chua’s equation near a triple-zero linear degeneracy. Zbl 1083.93020 Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 21 2003 A tame degenerate Hopf-pitchfork bifurcation in a modified van der Pol-Duffing oscillator. Zbl 0976.70016 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 20 2000 T-points in a \(\mathbb Z_2\)-symmetric electronic oscillator. I: Analysis. Zbl 1065.34038 Fernández-Sánchez, F.; Freire, E.; Rodríguez-Luis, A. J. 19 2002 On the Hopf-pitchfork bifurcation in the Chua’s equation. Zbl 1090.34545 Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 18 2000 Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator. Zbl 0928.70042 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 17 1998 A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation. Zbl 0943.34027 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 16 1999 Asymptotics of homoclinic bifurcation in a three-dimensional system. Zbl 0960.70019 Belhaq, M.; Houssni, M.; Freire, E.; Rodríguez-Luis, A. J. 14 2000 The non-transverse Shil’nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies. Zbl 0986.37041 Champneys, A. R.; Rodríguez-Luis, A. J. 13 1999 Hypernormal form calculation for triple-zero degeneracies. Zbl 0988.37062 Gamero, E.; Freire, E.; Rodríguez-Luis, A. J.; Ponce, E.; Algaba, A. 13 1999 Analysis of the T-point-Hopf bifurcation. Zbl 1158.34029 Fernández-Sánchez, F.; Freire, E.; Rodríguez-Luis, A. J. 11 2008 Multiparametric bifurcations in an enzyme-catalyzed reaction model. Zbl 1069.92009 Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J.; Fernández-Sánchez, F. 11 2005 On a codimension-three unfolding of the interaction of degenerate Hopf and pitchfork bifurcations. Zbl 0983.37057 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 11 1999 A bifurcation analysis of a simple electronic circuit. Zbl 1064.34030 Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J. 11 2005 Bi-spiraling homoclinic curves around a T-point in Chua’s equation. Zbl 1129.37308 Fernández-Sánchez, Fernando; Freire, Emilio; Rodríguez-Luis, Alejandro J. 11 2004 Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations. Zbl 0999.37035 Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Merino, M.; Rodríguez-Luis, A. J. 11 2002 A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form. Zbl 1430.37054 Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 11 2019 Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with \(D_4\) symmetry. Zbl 1397.37022 Qin, B. W.; Chung, K. W.; Rodríguez-Luis, A. J.; Belhaq, M. 10 2018 Resonances of periodic orbits in Rössler system in presence of a triple-zero bifurcation. Zbl 1145.37322 Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; Rodríguez-Luis, Alejandro J. 9 2007 First-order approximation for canard periodic orbits in a van der Pol electronic oscillator. Zbl 1066.34510 Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 9 1999 Takens-Bogdanov bifurcations of periodic orbits and Arnold’s tongues in a three-dimensional electronic model. Zbl 1090.37543 Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 9 2001 Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Zbl 1345.34069 Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J. 9 2015 Centers on center manifolds in the Lorenz, Chen and Lü systems. Zbl 1457.34061 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 9 2014 Numerical continuation of homoclinic orbits to non-hyperbolic equilibria in planar systems. Zbl 0983.70018 Freire, E.; Pizzaro, L.; Rodríguez-Luis, A. J. 8 2000 An exact homoclinic orbit and its connection with the Rössler system. Zbl 1396.37027 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 8 2015 Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Zbl 1489.37069 Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. 8 2015 High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. Zbl 1436.34035 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 8 2020 Analytical approximation of cuspidal loops using a nonlinear time transformation method. Zbl 1433.37019 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 8 2020 Closed curves of global bifurcations in Chua’s equation: a mechanism for their formation. Zbl 1056.37067 Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 7 2003 Analysis of the T-point-Hopf bifurcation in the Lorenz system. Zbl 1329.37082 Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 7 2015 Comment on “Sil’nikov chaos of the Liu system”. Zbl 1317.34083 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2011 Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms. Zbl 1453.37045 Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 7 2020 On Darboux polynomials and rational first integrals of the generalized Lorenz system. Zbl 1302.34001 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2014 An analytical and numerical study of a modified van der Pol oscillator. Zbl 1237.34059 Doedel, Eusebius J.; Freire Macías, Emilio; Gamero, Estanislao; Rodríguez-Luis, A. J. 6 2002 A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point. Zbl 1065.37019 Fernández-Sánchez, F.; Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J. 6 2003 Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. Zbl 1268.37017 Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 6 2012 Open-to-closed curves of saddle-node bifurcations of periodic orbits near a nontransversal T-point in Chua’s equation. Zbl 1142.34029 Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 5 2006 High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067 Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. 5 2021 Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method. Zbl 1482.34138 Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 5 2020 Comment on ‘Šilnikov-type orbits of Lorenz-family systems’. Zbl 1395.37020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2013 Comments on “Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces”. Zbl 1291.34080 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2014 High-order analysis of canard explosion in the Brusselator equations. Zbl 1447.34023 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 5 2020 Hopf bifurcations and their degeneracies in Chua’s equation. Zbl 1248.34059 Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 4 2011 Oscillation-sliding in a modified van der Pol-Duffing electronic oscillator. Zbl 1237.34049 Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 4 2002 Isolas, cusps and global bifurcations in an electronic oscillator. Zbl 0940.70018 Fernández-Sánchez, F.; Freire, E.; Rodríguez-Luis, A. J. 4 1997 Homoclinic connections near a Belyakov point in Chua’s equation. Zbl 1089.37019 Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 4 2005 Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system”. Zbl 1247.34072 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2012 Comments on “The Chen system revisited”. Zbl 1306.34020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2014 High-order study of the canard explosion in an aircraft ground dynamics model. Zbl 1459.34133 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 4 2020 Second period-doubling in a three-dimensional system. Zbl 0945.70538 Belhaq, M.; Freire, E.; Houssni, M.; Rodríguez-Luis, A. J. 3 1999 Numerical continuation of degenerate homoclinic orbits in planar systems. Zbl 0921.65050 Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J. 3 1999 A method for homoclinic and heteroclinic continuation in two and three dimensions. Zbl 0705.34053 Rodríguez-Luis, A. J.; Freire, E.; Ponce, E. 3 1990 Superluminal periodic orbits in the Lorenz system. Zbl 1510.34082 Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 3 2016 Homoclinic interactions near a triple-zero degeneracy in Chua’s equation. Zbl 1270.34113 Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2012 Analysis of the T-point-Hopf bifurcation with \(\mathbb Z_2\)-symmetry. Application to Chua’s equation. Zbl 1193.34078 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2010 Asymptotic expansions for a family of non-generic canards using parametric representation. Zbl 1524.34135 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 3 2020 Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang. Zbl 1319.37011 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Zbl 1277.65108 Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 2 2013 Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”. Zbl 1470.37040 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Numerical bifurcation analysis of electronic circuits. Zbl 1126.65107 Freire, Emilio; Rodríguez-Luis, Alejandro J. 1 2007 Hopf-zero bifurcation: Normal form calculation and application to an electronic oscillator. Zbl 0938.37514 Gamero, E.; Freire, E.; Rodríguez-Luis, A. J. 1 1993 Examples of non-degenerate and degenerate cuspidal loops in planar systems. Zbl 0930.34031 Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J. 1 1999 Comment on “Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems”. Zbl 1335.37011 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 1 2014 Comments on: “Invariant algebraic surfaces of the generalized Lorenz system”. Zbl 1323.34019 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 1 2015 Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system. Zbl 1500.34016 Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. 1 2022 Asymptotic expansions for a degenerate canard explosion. Zbl 1496.34094 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 1 2021 Study of a dynamical system with a strange attractor and invariant tori. Zbl 1470.37084 Algaba, Antonio; Merino, Manuel; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 1 2019 Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system. Zbl 1500.34016 Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. 1 2022 High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067 Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. 5 2021 Asymptotic expansions for a degenerate canard explosion. Zbl 1496.34094 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 1 2021 High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. Zbl 1436.34035 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 8 2020 Analytical approximation of cuspidal loops using a nonlinear time transformation method. Zbl 1433.37019 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 8 2020 Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms. Zbl 1453.37045 Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 7 2020 Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method. Zbl 1482.34138 Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 5 2020 High-order analysis of canard explosion in the Brusselator equations. Zbl 1447.34023 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 5 2020 High-order study of the canard explosion in an aircraft ground dynamics model. Zbl 1459.34133 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 4 2020 Asymptotic expansions for a family of non-generic canards using parametric representation. Zbl 1524.34135 Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 3 2020 A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form. Zbl 1430.37054 Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 11 2019 Study of a dynamical system with a strange attractor and invariant tori. Zbl 1470.37084 Algaba, Antonio; Merino, Manuel; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 1 2019 Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with \(D_4\) symmetry. Zbl 1397.37022 Qin, B. W.; Chung, K. W.; Rodríguez-Luis, A. J.; Belhaq, M. 10 2018 Superluminal periodic orbits in the Lorenz system. Zbl 1510.34082 Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 3 2016 Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Zbl 1345.34069 Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J. 9 2015 An exact homoclinic orbit and its connection with the Rössler system. Zbl 1396.37027 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 8 2015 Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Zbl 1489.37069 Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. 8 2015 Analysis of the T-point-Hopf bifurcation in the Lorenz system. Zbl 1329.37082 Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 7 2015 Comments on: “Invariant algebraic surfaces of the generalized Lorenz system”. Zbl 1323.34019 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 1 2015 Centers on center manifolds in the Lorenz, Chen and Lü systems. Zbl 1457.34061 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 9 2014 On Darboux polynomials and rational first integrals of the generalized Lorenz system. Zbl 1302.34001 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2014 Comments on “Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces”. Zbl 1291.34080 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2014 Comments on “The Chen system revisited”. Zbl 1306.34020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2014 Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang. Zbl 1319.37011 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”. Zbl 1470.37040 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Comment on “Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems”. Zbl 1335.37011 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 1 2014 Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system. Zbl 1323.37020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 32 2013 The Lü system is a particular case of the Lorenz system. Zbl 1301.37020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 24 2013 Comment on ‘Šilnikov-type orbits of Lorenz-family systems’. Zbl 1395.37020 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2013 Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Zbl 1277.65108 Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 2 2013 Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. Zbl 1268.37017 Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 6 2012 Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system”. Zbl 1247.34072 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2012 Homoclinic interactions near a triple-zero degeneracy in Chua’s equation. Zbl 1270.34113 Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2012 Comment on “Sil’nikov chaos of the Liu system”. Zbl 1317.34083 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2011 Hopf bifurcations and their degeneracies in Chua’s equation. Zbl 1248.34059 Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 4 2011 Analysis of the T-point-Hopf bifurcation with \(\mathbb Z_2\)-symmetry. Application to Chua’s equation. Zbl 1193.34078 Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2010 Analysis of the T-point-Hopf bifurcation. Zbl 1158.34029 Fernández-Sánchez, F.; Freire, E.; Rodríguez-Luis, A. J. 11 2008 Resonances of periodic orbits in Rössler system in presence of a triple-zero bifurcation. Zbl 1145.37322 Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; Rodríguez-Luis, Alejandro J. 9 2007 Numerical bifurcation analysis of electronic circuits. Zbl 1126.65107 Freire, Emilio; Rodríguez-Luis, Alejandro J. 1 2007 Open-to-closed curves of saddle-node bifurcations of periodic orbits near a nontransversal T-point in Chua’s equation. Zbl 1142.34029 Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 5 2006 Multiparametric bifurcations in an enzyme-catalyzed reaction model. Zbl 1069.92009 Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J.; Fernández-Sánchez, F. 11 2005 A bifurcation analysis of a simple electronic circuit. Zbl 1064.34030 Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J. 11 2005 Homoclinic connections near a Belyakov point in Chua’s equation. Zbl 1089.37019 Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 4 2005 Bi-spiraling homoclinic curves around a T-point in Chua’s equation. Zbl 1129.37308 Fernández-Sánchez, Fernando; Freire, Emilio; Rodríguez-Luis, Alejandro J. 11 2004 Some results on Chua’s equation near a triple-zero linear degeneracy. Zbl 1083.93020 Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 21 2003 Closed curves of global bifurcations in Chua’s equation: a mechanism for their formation. Zbl 1056.37067 Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 7 2003 A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point. Zbl 1065.37019 Fernández-Sánchez, F.; Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J. 6 2003 A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. Zbl 1043.37042 Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A. 34 2002 T-points in a \(\mathbb Z_2\)-symmetric electronic oscillator. I: Analysis. Zbl 1065.34038 Fernández-Sánchez, F.; Freire, E.; Rodríguez-Luis, A. J. 19 2002 Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations. Zbl 0999.37035 Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Merino, M.; Rodríguez-Luis, A. J. 11 2002 An analytical and numerical study of a modified van der Pol oscillator. Zbl 1237.34059 Doedel, Eusebius J.; Freire Macías, Emilio; Gamero, Estanislao; Rodríguez-Luis, A. J. 6 2002 Oscillation-sliding in a modified van der Pol-Duffing electronic oscillator. Zbl 1237.34049 Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 4 2002 Takens-Bogdanov bifurcations of periodic orbits and Arnold’s tongues in a three-dimensional electronic model. Zbl 1090.37543 Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 9 2001 A tame degenerate Hopf-pitchfork bifurcation in a modified van der Pol-Duffing oscillator. Zbl 0976.70016 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 20 2000 On the Hopf-pitchfork bifurcation in the Chua’s equation. Zbl 1090.34545 Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 18 2000 Asymptotics of homoclinic bifurcation in a three-dimensional system. Zbl 0960.70019 Belhaq, M.; Houssni, M.; Freire, E.; Rodríguez-Luis, A. J. 14 2000 Numerical continuation of homoclinic orbits to non-hyperbolic equilibria in planar systems. Zbl 0983.70018 Freire, E.; Pizzaro, L.; Rodríguez-Luis, A. J. 8 2000 A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation. Zbl 0943.34027 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 16 1999 The non-transverse Shil’nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies. Zbl 0986.37041 Champneys, A. R.; Rodríguez-Luis, A. J. 13 1999 Hypernormal form calculation for triple-zero degeneracies. Zbl 0988.37062 Gamero, E.; Freire, E.; Rodríguez-Luis, A. J.; Ponce, E.; Algaba, A. 13 1999 On a codimension-three unfolding of the interaction of degenerate Hopf and pitchfork bifurcations. Zbl 0983.37057 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 11 1999 First-order approximation for canard periodic orbits in a van der Pol electronic oscillator. Zbl 1066.34510 Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 9 1999 Second period-doubling in a three-dimensional system. Zbl 0945.70538 Belhaq, M.; Freire, E.; Houssni, M.; Rodríguez-Luis, A. J. 3 1999 Numerical continuation of degenerate homoclinic orbits in planar systems. Zbl 0921.65050 Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J. 3 1999 Examples of non-degenerate and degenerate cuspidal loops in planar systems. Zbl 0930.34031 Freire, E.; Pizarro, L.; Rodríguez-Luis, A. J. 1 1999 Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator. Zbl 0928.70042 Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 17 1998 Isolas, cusps and global bifurcations in an electronic oscillator. Zbl 0940.70018 Fernández-Sánchez, F.; Freire, E.; Rodríguez-Luis, A. J. 4 1997 A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Sil’nikov. Zbl 0809.58040 Freire, E.; Rodríguez-Luis, A. J.; Gamero, E.; Ponce, E. 26 1993 Hopf-zero bifurcation: Normal form calculation and application to an electronic oscillator. Zbl 0938.37514 Gamero, E.; Freire, E.; Rodríguez-Luis, A. J. 1 1993 A method for homoclinic and heteroclinic continuation in two and three dimensions. Zbl 0705.34053 Rodríguez-Luis, A. J.; Freire, E.; Ponce, E. 3 1990 all cited Publications top 5 cited Publications all top 5 Cited by 390 Authors 51 Rodríguez-Luis, Alejandro J. 44 Algaba, Antonio 29 Merino, Manuel 26 Fernández-Sánchez, Fernando 14 Freire Macías, Emilio 13 Qin, Bo-Wei 12 Chung, Kwok-Wai 8 Gamero, Estanislao 6 Barrio, Roberto 6 Liu, Xingbo 5 Carmona, Victoriano 5 Gazor, Majid 5 Llibre, Jaume 5 Moiola, Jorge Luis 5 Teruel, Antonio E. 5 Zhang, Fuchen 4 Belhaq, Mohamed 4 García-Medina, Elisabeth 4 Ibáñez, Santiago 4 Knobloch, Edgar 4 Kuznetsov, Yuri Alexandrovich 4 Li, Chunbiao 4 Rodrigues, Alexandre A. P. 4 Shoghi, Ahmad 4 Sprott, Julien Clinton 4 Wang, Haijun 3 Bella, Giovanni 3 Bi, Qinsheng 3 Domínguez-Moreno, María C. 3 Drubi, Fátima 3 Fernández-García, Soledad 3 Guo, Shangjiang 3 Kapitaniak, Tomasz 3 Krauskopf, Bernd 3 Lamb, Jeroen S. W. 3 Li, Jing 3 Li, Xianyi 3 Liao, Xiaofeng 3 Liu, Xia 3 Mokhtari, Fahimeh 3 Pizarro, Luis 3 Ponce, Enrique 3 Rocha, Ronilson 3 Serrano, Sergio E. 3 Shilnikov, Andrey L. 3 Su, Juan 3 Wang, Duo 3 Webster, Kevin N. 3 Yang, Shuangling 3 Zhang, Guangyun 2 Alonso, Diego M. 2 Blesa, Fernando 2 Bykov, V. V. 2 Chen, Guanrong 2 de Carvalho Braga, Denis 2 De Feo, Oscar 2 García, Isaac A. 2 Han, Maoan 2 Horikawa, Yo 2 Huang, Wentao 2 Kitajima, Hiroyuki 2 Knobloch, Jürgen 2 Kou, Liying 2 Lakrad, Faouzi 2 Liu, Junli 2 Liu, Xuanliang 2 Marwan, Muhammad 2 Mattana, Paolo 2 Maza, Susanna 2 Meddour, Lotfi 2 Medrano-T, Rene Orlando 2 Meijer, Hil G. E. 2 Mello, Luis Fernando O. 2 Mu, Chunlai 2 Osinga, Hinke Maria 2 Páez Chávez, Joseph Nikolai 2 Porter, Jeff 2 Pusuluri, Krishna 2 Qu, Jingjia 2 Riaza, Ricardo 2 Robbio, Federico I. 2 Sanders, Jan A. 2 Shafer, Douglas S. 2 Teixeira, Marco Antonio 2 Xu, Yancong 2 Yu, Pei 2 Zhang, Tonghua 1 Achouri, Houssem 1 Afsharnejad, Zahra 1 Ahmad, Salman 1 Al-Hdaibat, Bashir 1 Al Saadi, Fahad 1 Alrihieli, Haifaa F. 1 Aouiti, Chaouki 1 Aqeel, Muhammad 1 Astakhov, Vladimir V. 1 Atencia, Miguel A. 1 Bao, Bocheng 1 Bao, Han 1 Barboza, Ruy ...and 290 more Authors all top 5 Cited in 67 Serials 65 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 22 Physica D 20 Nonlinear Dynamics 14 Chaos, Solitons and Fractals 11 Chaos 9 Journal of Differential Equations 9 Communications in Nonlinear Science and Numerical Simulation 6 Physics Letters. 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(English Edition) 2 Journal of Dynamics and Differential Equations 2 Journal of Nonlinear Science 2 Journal of Difference Equations and Applications 2 Journal of Mathematical Chemistry 2 Dynamical Systems 2 Journal of Systems Science and Complexity 2 Advances in Difference Equations 2 Journal of Applied Analysis and Computation 1 Communications in Mathematical Physics 1 Journal of Statistical Physics 1 Nonlinearity 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Automatica 1 Numerische Mathematik 1 Theoretical Population Biology 1 Chinese Annals of Mathematics. Series B 1 Journal of Symbolic Computation 1 Mathematical and Computer Modelling 1 Neural Computation 1 Economics Letters 1 Applied Mathematical Modelling 1 Computational and Applied Mathematics 1 Bulletin des Sciences Mathématiques 1 Mathematical Problems in Engineering 1 Soft Computing 1 Proceedings of the Royal Society of London. Series A. 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Second Series 1 Journal of Dynamical Systems and Geometric Theories 1 Journal of Statistical Mechanics: Theory and Experiment 1 Mathematical Biosciences and Engineering 1 Advances in Mathematical Physics 1 International Journal of Applied and Computational Mathematics 1 AIMS Mathematics all top 5 Cited in 26 Fields 193 Ordinary differential equations (34-XX) 146 Dynamical systems and ergodic theory (37-XX) 29 Biology and other natural sciences (92-XX) 20 Numerical analysis (65-XX) 20 Mechanics of particles and systems (70-XX) 16 Systems theory; control (93-XX) 15 Information and communication theory, circuits (94-XX) 6 Computer science (68-XX) 6 Optics, electromagnetic theory (78-XX) 5 Partial differential equations (35-XX) 5 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year