Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system. (English) Zbl 1500.34016 Commun. Nonlinear Sci. Numer. Simul. 111, Article ID 106482, 23 p. (2022). Reviewer: Yong Ye (Shenzhen) MSC: 34A34 34C20 34C23 34D45 34C37 34E10 34C05 37D45 PDFBibTeX XMLCite \textit{A. Algaba} et al., Commun. Nonlinear Sci. Numer. Simul. 111, Article ID 106482, 23 p. (2022; Zbl 1500.34016) Full Text: DOI
Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. (English) Zbl 1478.34067 SIAM J. Appl. Dyn. Syst. 20, No. 1, 403-437 (2021). Reviewer: Tao Li (Chengdu) MSC: 34E05 34E10 34C37 37M20 41A60 34C20 34C23 PDFBibTeX XMLCite \textit{B. W. Qin} et al., SIAM J. Appl. Dyn. Syst. 20, No. 1, 403--437 (2021; Zbl 1478.34067) Full Text: DOI
Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. High-order analysis of canard explosion in the Brusselator equations. (English) Zbl 1447.34023 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 5, Article ID 2050078, 10 p. (2020). MSC: 34A45 34C23 34E17 34C20 34E05 34E10 PDFBibTeX XMLCite \textit{B.-W. Qin} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 5, Article ID 2050078, 10 p. (2020; Zbl 1447.34023) Full Text: DOI
Algaba, Antonio; Merino, Manuel; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. Study of a dynamical system with a strange attractor and invariant tori. (English) Zbl 1470.37084 Phys. Lett., A 383, No. 13, 1441-1449 (2019). MSC: 37J40 34C28 PDFBibTeX XMLCite \textit{A. Algaba} et al., Phys. Lett., A 383, No. 13, 1441--1449 (2019; Zbl 1470.37084) Full Text: DOI
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. Comments on “The Chen system revisited”. (English) Zbl 1306.34020 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 21, No. 4-5, 275-280 (2014). MSC: 34A34 34C20 37D45 34C28 PDFBibTeX XMLCite \textit{A. Algaba} et al., Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 21, No. 4--5, 275--280 (2014; Zbl 1306.34020) Full Text: Link
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. On Darboux polynomials and rational first integrals of the generalized Lorenz system. (English) Zbl 1302.34001 Bull. Sci. Math. 138, No. 3, 317-322 (2014). Reviewer: Jaume Giné (Lleida) MSC: 34A05 34A34 34C20 34C14 PDFBibTeX XMLCite \textit{A. Algaba} et al., Bull. Sci. Math. 138, No. 3, 317--322 (2014; Zbl 1302.34001) Full Text: DOI
Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. Hopf bifurcations and their degeneracies in Chua’s equation. (English) Zbl 1248.34059 Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 9, 2749-2763 (2011). MSC: 34C60 34C23 34C20 PDFBibTeX XMLCite \textit{A. Algaba} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 9, 2749--2763 (2011; Zbl 1248.34059) Full Text: DOI
Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J. A bifurcation analysis of a simple electronic circuit. (English) Zbl 1064.34030 Commun. Nonlinear Sci. Numer. Simul. 10, No. 2, 169-178 (2005). Reviewer: Ricardo Riaza (Madrid) MSC: 34C60 37G10 34C23 PDFBibTeX XMLCite \textit{A. Algaba} et al., Commun. Nonlinear Sci. Numer. Simul. 10, No. 2, 169--178 (2005; Zbl 1064.34030) Full Text: DOI
Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. Some results on Chua’s equation near a triple-zero linear degeneracy. (English) Zbl 1083.93020 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 3, 583-608 (2003). Reviewer: Fabio Bagagiolo (Trento) MSC: 93C10 34C20 34C23 PDFBibTeX XMLCite \textit{A. Algaba} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 3, 583--608 (2003; Zbl 1083.93020) Full Text: DOI
Doedel, Eusebius J.; Freire Macías, Emilio; Gamero, Estanislao; Rodríguez-Luis, A. J. An analytical and numerical study of a modified van der Pol oscillator. (English) Zbl 1237.34059 J. Sound Vib. 256, No. 4, 755-771 (2002). MSC: 34C15 34C20 34C23 PDFBibTeX XMLCite \textit{E. J. Doedel} et al., J. Sound Vib. 256, No. 4, 755--771 (2002; Zbl 1237.34059) Full Text: DOI
Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A. A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. (English) Zbl 1043.37042 Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 12, 2799-2820 (2002). MSC: 37G10 34C20 34C23 34C37 37G05 58K50 PDFBibTeX XMLCite \textit{E. Freire} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 12, 2799--2820 (2002; Zbl 1043.37042) Full Text: DOI
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. On a codimension-three unfolding of the interaction of degenerate Hopf and pitchfork bifurcations. (English) Zbl 0983.37057 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 7, 1333-1362 (1999). Reviewer: Boris V.Loginov (Ankara) MSC: 37G15 34C60 37G40 58K45 58K50 58E09 PDFBibTeX XMLCite \textit{A. Algaba} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 7, 1333--1362 (1999; Zbl 0983.37057) Full Text: DOI
Gamero, E.; Freire, E.; Rodríguez-Luis, A. J.; Ponce, E.; Algaba, A. Hypernormal form calculation for triple-zero degeneracies. (English) Zbl 0988.37062 Bull. Belg. Math. Soc. - Simon Stevin 6, No. 3, 357-368 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37G05 34C20 34C60 PDFBibTeX XMLCite \textit{E. Gamero} et al., Bull. Belg. Math. Soc. - Simon Stevin 6, No. 3, 357--368 (1999; Zbl 0988.37062)
Champneys, A. R.; Rodríguez-Luis, A. J. The non-transverse Shil’nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies. (English) Zbl 0986.37041 Physica D 128, No. 2-4, 130-158 (1999). Reviewer: Lev Lerman (Nizhny Novgorod) MSC: 37G20 37G15 34C37 34C23 37J40 70H08 37J25 PDFBibTeX XMLCite \textit{A. R. Champneys} and \textit{A. J. Rodríguez-Luis}, Physica D 128, No. 2--4, 130--158 (1999; Zbl 0986.37041) Full Text: DOI
Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation. (English) Zbl 0943.34027 Nonlinearity 12, No. 4, 1177-1206 (1999). MSC: 34C23 37G05 34C15 34C37 37G10 PDFBibTeX XMLCite \textit{A. Algaba} et al., Nonlinearity 12, No. 4, 1177--1206 (1999; Zbl 0943.34027) Full Text: DOI
Gamero, E.; Freire, E.; Rodríguez-Luis, A. J.; Algaba, A. Normal forms for the Hopf-zero degeneracy in reversible systems. (English) Zbl 0957.37045 Magalhães, L. (ed.) et al., International conference on differential equations. Papers from the conference, EQUADIFF 95, Lisboa, Portugal, July 24-29, 1995. Singapore: World Scientific. 356-363 (1998). MSC: 37G40 37G05 37C27 34C25 34C20 34C14 PDFBibTeX XMLCite \textit{E. Gamero} et al., in: International conference on differential equations. Papers from the conference, EQUADIFF 95, Lisboa, Portugal, July 24--29, 1995. Singapore: World Scientific. 356--363 (1998; Zbl 0957.37045)
Gamero, E.; Freire, E.; Rodríguez-Luis, A. J. Hopf-zero bifurcation: Normal form calculation and application to an electronic oscillator. (English) Zbl 0938.37514 Perelló, C. (ed.) et al., International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991. Singapore: World Scientific. 517-524 (1993). MSC: 37G99 34C15 34C20 34C23 PDFBibTeX XMLCite \textit{E. Gamero} et al., in: International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991. Singapore: World Scientific. 517--524 (1993; Zbl 0938.37514)