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Contributions to codimension k bifurcations in dynamical systems theory

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Publications

On the limit cycles of a class of discontinuous piecewise linear differential systems

Author(s): Jaume Llibre, Lucyjane de A. S. Menezes
Published in: Discrete & Continuous Dynamical Systems - B, Issue 25/5, 2020, Page(s) 1835-1858, ISSN 1553-524X
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcdsb.2020005

Stability and Bifurcations in a Nutrient–Phytoplankton–Zooplankton Model with Delayed Nutrient Recycling with Gamma Distribution

Author(s): Mihaela Sterpu; Carmen Rocşoreanu; Raluca Efrem; Sue Ann Campbell
Published in: Mathematics, Vol 11, Iss 13, p 2911 (2023), Issue 21, 2023, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math11132911

Criticality via first order development of the period constants

Author(s): Iván Sánchez-Sánchez, Joan Torregrosa
Published in: Nonlinear Analysis, Issue 203, 2021, Page(s) 112164, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2020.112164

Piecewise linear differential systems with an algebraic line of separation

Author(s): A. Gasull, J. Torregrosa, X. Zhang
Published in: Electronic Journal of Differential Equations, Issue 19, 2020, Page(s) 1-14, ISSN 1072-6691
Publisher: Texas State University - San Marcos

On the birth and death of algebraic limit cycles in quadratic differential systems

Author(s): JAUME LLIBRE, REGILENE OLIVEIRA, YULIN ZHAO
Published in: European Journal of Applied Mathematics, Issue 32/2, 2021, Page(s) 317-336, ISSN 0956-7925
Publisher: Cambridge University Press
DOI: 10.1017/s0956792520000145

Analysis of a class of Kolmogorov systems

Author(s): G. Tigan, C. Lazureanu, F. Munteanu, C. Sterbeti, A. Florea
Published in: Nonlinear Analysis: Real World Applications, Issue 57, 2021, ISSN 1878-5719
Publisher: Elsevier
DOI: 10.1016/j.nonrwa.2020.103202

Dynamics of a family of Lotka–Volterra systems in R 3

Author(s): Jaume Llibre, Y. Paulina Martínez
Published in: Nonlinear Analysis, Issue 199, 2020, Page(s) 111915, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2020.111915

Bifurcation diagrams in a class of Kolmogorov systems

Author(s): G. Tigan, C. Lazureanu, F. Munteanu, C. Sterbeti, A. Florea
Published in: Nonlinear Analysis: Real World Applications, Issue 56, 2020, ISSN 1878-5719
Publisher: Elsevier
DOI: 10.1016/j.nonrwa.2020.103154

Limit cycles of discontinuous piecewise differential systems formed by linear centers in R 2 and separated by two circles

Author(s): Maria Elisa Anacleto, Jaume Llibre, Claudia Valls, Claudio Vidal
Published in: Nonlinear Analysis: Real World Applications, Issue 60, 2021, Page(s) 103281, ISSN 1468-1218
Publisher: Elsevier BV
DOI: 10.1016/j.nonrwa.2020.103281

Final evolutions for simplified multistrain/two-stream model for tuberculosis and dengue fever

Author(s): Jaume Llibre, Regilene D.S. Oliveira, Claudia Valls
Published in: Chaos, Solitons & Fractals, Issue 118, 2019, Page(s) 181-186, ISSN 0960-0779
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2018.11.022

Global dynamics of the Buckingham’s two-body problem

Author(s): Jaume Llibre, Claudia Valls, Claudio Vidal
Published in: Astrophysics and Space Science, Issue 363/12, 2018, Page(s) Article 255, ISSN 0004-640X
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10509-018-3475-y

Invariant Algebraic Surfaces and Hopf Bifurcation of a Finance Model

Author(s): Murilo R. Cândido, Jaume Llibre, Claudia Valls
Published in: International Journal of Bifurcation and Chaos, Issue 28/12, 2018, Page(s) 1850150, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s021812741850150x

Phase portraits of continuous piecewise linear Liénard differential systems with three zones

Author(s): Shimin Li, Jaume Llibre
Published in: Chaos, Solitons & Fractals, Issue 120, 2019, Page(s) 149-157, ISSN 0960-0779
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2018.12.037

Bounded polynomial vector fields in R 2 and R n

Author(s): Luis Barreira, Jaume Llibre, Claudia Valls
Published in: Journal of Differential Equations, Issue 268/8, 2020, Page(s) 4416-4422, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.10.023

Approximations of the Heteroclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two. Application to a Liénard Equation

Author(s): Carmen Rocşoreanu, Mihaela Sterpu
Published in: International Journal of Bifurcation and Chaos, Issue 29/06, 2019, Page(s) 1950074, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127419500743

Nilpotent Global Centers of Linear Systems with Cubic Homogeneous Nonlinearities

Author(s): J. D. García-Saldaña, Jaume Llibre, Claudia Valls
Published in: International Journal of Bifurcation and Chaos, Issue 30/01, 2020, Page(s) 2050010, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127420500108

Topological entropy of continuous self-maps on closed surfaces

Author(s): Juan Luis García Guirao, Jaume Llibre, Wei Gao
Published in: Journal of Difference Equations and Applications, Issue 26/2, 2020, Page(s) 203-208, ISSN 1023-6198
Publisher: Taylor & Francis
DOI: 10.1080/10236198.2019.1710141

Limit cycles created by piecewise linear centers

Author(s): Jaume Llibre, Xiang Zhang
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue 29/5, 2019, Page(s) 053116, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/1.5086018

Limit cycles in 4-star-symmetric planar piecewise linear systems

Author(s): Claudio A. Buzzi, Joao C. Medrado, Joan Torregrosa
Published in: Journal of Differential Equations, Issue 268/5, 2020, Page(s) 2414-2434, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.09.008

Bifurcations from families of periodic solutions in piecewise differential systems

Author(s): Jaume Llibre, Douglas D. Novaes, Camila A.B. Rodrigues
Published in: Physica D: Nonlinear Phenomena, Issue 404, 2020, Page(s) 132342, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2020.132342

Limit cycles for two classes of control piecewise linear differential systems

Author(s): Jaume Llibre, Regilene D. Oliveira, Camila Ap. B. Rodrigues
Published in: São Paulo Journal of Mathematical Sciences, Issue 36, 2020, Page(s) 1-17, ISSN 1982-6907
Publisher: Springer
DOI: 10.1007/s40863-020-00163-7

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