Contributions to codimension k bifurcations in dynamical systems theory

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Publicaciones

A Bendixon–Dulac theorem for some piecewise systems

Autores: Leonardo P C da Cruz; Joan Torregrosa
Publicado en: Nonlinearity, 2020, ISSN 0951-7715
Editor: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab6812

Analysis of a map-based neuronal model

Autores: G. Tigan, R. Efrem
Publicado en: Journal of Difference Equations and Applications, 2020, ISSN 1563-5120
Editor: Taylor & Francis
DOI: 10.1080/10236198.2020.1780219

On the Jacobi Stability of Two SIR Epidemic Patterns With Demography

Autores: Florian Munteanu
Publicado en: Symmetry, Edición 9, 2023, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.20944/preprints202304.1139.v1

Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials

Autores: Jaume Llibre; Fabao Gao; Fabao Gao
Publicado en: Eur. Phys. J. C Part. Fields, 2020, ISSN 1434-6044
Editor: Springer Verlag
DOI: 10.1140/epjc/s10052-020-7714-3

Dynamics and Darboux Integrability of the D2 Polynomial Vector Fields of Degree 2 in $\mathbb {R}^{3}$

Autores: Jean-Marc Ginoux; Jaume Llibre; Claudia Valls
Publicado en: Math. Phys. Anal. Geom., Edición 16, 2021, ISSN 1385-0172
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11040-020-09372-0

Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariantq

Autores: Jaume Llibre; Regilene D. S. Oliveira; Camila A. B. Rodrigues
Publicado en: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, ISSN 1072-6691
Editor: Texas State University - San Marcos
DOI: 10.58997/ejde.2021.69

Limit Cycles of Some Families of Discontinuous Piecewise Differential Systems Separated by a Straight Line

Autores: Louiza Baymout, Rebiha Benterki, Jaume Llibre
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2023, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127423501663

Phase portraits of two classes of Liénard equations

Autores: Jie Li, Jaume Llibre
Publicado en: Boletin de la Sociedad Matematica Mexicana, 2023, ISSN 1405-213X
Editor: Birkhäuser Verlag
DOI: 10.1007/s40590-022-00479-8

Phase portraits of an SIR epidemic model

Autores: Jaume Llibre, Tayeb Salhi
Publicado en: Applicable Analysis. An International Journal, 2024, ISSN 0003-6811
Editor: Taylor & Francis
DOI: 10.1080/00036811.2023.2235390

Periodic orbits of the planar anisotropic Manev problem and of the perturbed hydrogen atom problem

Autores: Jaume Llibre, Pengfei Yuan
Publicado en: Qual. Theory Dyn. Syst., 2019, ISSN 1575-5460
Editor: Springer Verlag
DOI: 10.1007/s12346-019-00322-y

Limit cycles on piecewise smooth vector fields with coupled rigid centers

Autores: Tiago Carvalho, Luiz Fernando Gonçalves, Jaume Llibre
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Edición 16 issues/vol./yr., 2021, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127421502242

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

Autores: Jaume Llibre, Lucyjane de A. S. Menezes
Publicado en: Discrete & Continuous Dynamical Systems - B, Edición 25/5, 2020, Página(s) 1835-1858, ISSN 1553-524X
Editor: 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

Autores: Mihaela Sterpu; Carmen Rocşoreanu; Raluca Efrem; Sue Ann Campbell
Publicado en: Mathematics, Vol 11, Iss 13, p 2911 (2023), Edición 21, 2023, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math11132911

The Functional Expansion Approach for Solving NPDEs as a Generalization of the Kudryashov and G0/G Methods

Autores: C. Ionescu, C. N. Babalic, R. Constantinescu, R. Efrem
Publicado en: Symmetry, 2022, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym14040827

Criticality via first order development of the period constants

Autores: Iván Sánchez-Sánchez, Joan Torregrosa
Publicado en: Nonlinear Analysis, Edición 203, 2021, Página(s) 112164, ISSN 0362-546X
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.na.2020.112164

A survey on algebraic and explicit non-algebraic limit cycles in planar differential systemsAuthor links open overlay panel

Autores: Jaume Llibre, Xiang Zhang
Publicado en: Expositiones Mathematicae, 2021, ISSN 0723-0869
Editor: Elsevier BV
DOI: 10.1016/j.exmath.2020.03.001

Limit cycles of a continuous piecewise differential system formed by aquadratic center and two linear centers

Autores: M. E. Anacleto, J. Llibre, C. Valls, C. Vidal
Publicado en: Boletín de la Sociedad Matemática Mexicana, 2023, ISSN 2296-4495
Editor: Springer
DOI: 10.1007/s40590-023-00501-7

The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems

Autores: Meriem Barkat, Rebiha Benterki, Jaume Llibre
Publicado en: Nonlinear Dynam., 2023, ISSN 0924-090X
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11071-022-07891-9

Analyzing the Jacobi Stability of Lü’s Circuit System

Autores: Munteanu, Florian
Publicado en: Symmetry, Edición 23, 2022, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym14061248

The Impact of the COVID-19 Pandemic on Electricity Consumption and Economic Growth in Romania

Autores: Georgeta Soava; Anca Mehedintu; Mihaela Sterpu; Eugenia Grecu
Publicado en: Energies, 2021, ISSN 1996-1073
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/en14092394

Polynomial Liénard systems with a nilpotent global center

Autores: Isaac A. García; Jaume Llibre
Publicado en: Rendiconti del Circolo Matematico di Palermo Series 2, Edición 6, 2023, ISSN 0009-725X
Editor: Circolo Matematico di Palermo
DOI: 10.1007/s12215-022-00850-8

Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems

Autores: Jie Li; Jaume Llibre
Publicado en: Differ. Equ. Dyn. Syst., Edición 1, 2023, ISSN 0971-3514
Editor: Research Square Publications
DOI: 10.1007/s12591-023-00666-7

Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line

Autores: L. P. C. da Cruz, J. Torregrosa, , Journal of Mathematical Analysis and Applications, 514 (2022) 126256.
Publicado en: Journal of Mathematical Analysis and Applications, Edición 514, 2022, ISSN 1096-0813
Editor: Elsevier
DOI: 10.1016/j.jmaa.2022.126256

The Extended 16th Hilbert Problem for Discontinuous Piecewise Linear Centers Separated by a Nonregular Line

Autores: M. Esteban, J. Llibre, C. Valls
Publicado en: International Journal of Bifurcation and Chaos, 2021, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127421502254

A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–prey System by the KCC Geometric Theory

Autores: Florian Munteanu
Publicado en: https://www.preprints.org/manuscript/202208.0129/v1, Edición 19, 2022, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.20944/preprints202208.0129.v1

The discontinuous matching of two globally asymptotically stable crossing piecewise smooth systems in the plane do not produce in general a piecewise differential system globally asymptotically stable

Autores: Denis de Carvalho Braga, Fabio Scalco Dias, Jaume Llibre, Luis Fernando Mello
Publicado en: São Paulo Journal of Mathematical Sciences, 2023, ISSN 1982-6907
Editor: Springer
DOI: 10.1007/s40863-023-00368-6

Limit Cycles Bifurcating from a Family of Reversible Quadratic Centers via Averaging Theory

Autores: Jaume Llibre; Arefeh Nabavi; Marzieh Mousavi
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Edición 19, 2020, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127420500510

Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4

Autores: Jaume Llibre, Yuzhou Tian
Publicado en: Discrete Contin. Dyn. Syst. Ser. B, Edición 12 issues/vol./yr., 2021, ISSN 1531-3492
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/dcdsb.2021228

Applied higher-order elliptic problems with nonstandard growth structure

Autores: Maria-Magdalena Boureanu, Alejandro Vélez-Santiago
Publicado en: Applied Mathematics Letters, 2022, ISSN 0893-9659
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.aml.2021.107603

Melnikov functions of arbitrary order for piecewise smooth differential systems in Rn and applications

Autores: X. Chen, T. Li, J. Llibre
Publicado en: Journal of Differential Equations, 2022, ISSN 1090-2732
Editor: Elsevier
DOI: 10.1016/j.jde.2022.01.019

An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems

Autores: Belén García, JaumeLlibre, Antón Lombardero, Jesús Suárez Pérez del Río
Publicado en: J. Symbolic Comput., 2019, ISSN 0747-7171
Editor: Academic Press
DOI: 10.1016/j.jsc.2018.08.006

Existence and uniqueness for a semilinear sixth-order

Autores: C-P. Danet
Publicado en: Electronic Journal of Qualitative Theory of Differential Equations, 2022, ISSN 1417-3875
Editor: Szegedi Tudomanyegyetern/University of Szeged
DOI: 10.14232/ejqtde.2022.1.53

A family of periodic orbits for the extended Hamiltonian system of the Van der Pol oscillator

Autores: Jean-Marc Ginoux, Jaume Llibre
Publicado en: J. Geom. Phys., Edición 12 vols./yr., 2023, ISSN 0393-0440
Editor: Elsevier BV
DOI: 10.1016/j.geomphys.2022.104705

Phase Portraits of a Class of Cubic Systems with an Ellipse and a Straight Line as Invariant Algebraic Curves

Autores: Ali Bakhshalizadeh, Jaume Llibre
Publicado en: Differential Equations and Dynamical Systems, 2024, ISSN 0971-3514
Editor: Research Square Publications
DOI: 10.1007/s12591-022-00597-9

Phase Portraits of the Leslie-Gower System

Autores: Llibre, Jaume||; Valls, Clàudia||
Publicado en: Acta Mathematica Scientia, Edición 9, 2022, ISSN 0252-9602
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10473-022-0502-4

Analysis of a Class of Lotka–Volterra Systems

Autores: G Moza, D Constantinescu, R Efrem, L Bucur, R Constantinescu
Publicado en: Qualitative theory of dynamical systems, Edición 21, 2022, ISSN 1662-3592
Editor: Springer
DOI: 10.1007/s12346-022-00563-4

Piecewise linear differential systems with an algebraic line of separation

Autores: A. Gasull, J. Torregrosa, X. Zhang
Publicado en: Electronic Journal of Differential Equations, Edición 19, 2020, Página(s) 1-14, ISSN 1072-6691
Editor: Texas State University - San Marcos

Dynamics of a Generalized Rayleigh System

Autores: Maíra Duran Baldissera, Jaume Llibre, Regilene Oliveira
Publicado en: Differential Equations and Dynamical Systems,, 2024, ISSN 0971-3514
Editor: Research Square Publications
DOI: 10.1007/s12591-022-00604-z

Phase Portraits of Families VII and VIII of the Quadratic Systems

Autores: Laurent Cairó; Jaume Llibre
Publicado en: Axioms, Edición 3, 2023, ISSN 2075-1680
Editor: MDPI
DOI: 10.3390/axioms12080756

Generalized analytic integrability of a class of polynomial differential systems in C2

Autores: Jaume Llibre, Yuzhou Tian
Publicado en: Acta Appl. Math., Edición 6 vols./yr, 2021, ISSN 0167-8019
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10440-021-00407-4

Bifurcation diagrams and global phase portraits for some hamiltonian systems with rational potentials

Autores: Ting Chen, Jaume Llibre
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2018, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127418501687

Admissible Perturbations of a Generalized Langford System

Autores: Eduard Musafirov; Alexander Grin; Andrei Pranevich
Publicado en: International Journal of Bifurcation and Chaos, 2022, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127422500389

Periodic solutions of a class of Duffing differential equations

Autores: Rebiha Benterki, Jaume Llibre
Publicado en: Journal of Nonlinear Modeling and Analysis, 2019, ISSN 2562-2854
Editor: Zhejiang Normal University
DOI: 10.12150/jnma.2019.167

Next in Surgical Data Science: Autonomous Non-Technical Skill Assessment in Minimally Invasive Surgery Training

Autores: Renáta Nagyné Elek; Tamás Haidegger
Publicado en: Journal of Clinical Medicine, Edición 6, 2022, ISSN 2077-0383
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/jcm11247533

About the Jacobi Stability of a Generalized Hopf–Langford System through the Kosambi–Cartan–Chern Geometric Theory

Autores: Florian Munteanu; Alexander Grin; Eduard Musafirov; Andrei Pranevich; Cătălin Şterbeţi
Publicado en: Symmetry, Edición 10, 2023, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym15030598

LIMIT CYCLES OF THE DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS ON THE CYLINDER

Autores: Li, Jie; Llibre, Jaume||
Publicado en: J. Appl. Anal. Comput., Edición 11, 2022, ISSN 2156-907X
Editor: Wilmington Sci. Publ. Shanghai Norm. Univ.
DOI: 10.11948/20220031

An analysis of two degenerate double-Hopf bifurcations

Autores: Gheorghe Moza, Mihaela Sterpu , Carmen Rocşoreanu
Publicado en: Electronic Research Archive, Edición 30, 2022, ISSN 2688-1594
Editor: AIMS Press
DOI: 10.3934/era.2022020

Entropy and periods for continuous graph maps, Computational and Applied Mathematics

Autores: J. Llibre, V.F. Sirvent
Publicado en: Computational and Applied Mathematics, 2021, ISSN 1807-0302
Editor: Springer
DOI: 10.1007/s40314-021-01677-2

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

Autores: JAUME LLIBRE, REGILENE OLIVEIRA, YULIN ZHAO
Publicado en: European Journal of Applied Mathematics, Edición 32/2, 2021, Página(s) 317-336, ISSN 0956-7925
Editor: Cambridge University Press
DOI: 10.1017/s0956792520000145

Dynamics of a four-dimensional economic model

Autores: G Moza, O Brandibur, A Găină
Publicado en: Mathematics, Edición 11, 2023, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math11040797

Orbitally symmetric systems with applications to planar centers

Autores: Bastos, Jefferson L. R.||; Buzzi, Claudio||; Torregrosa, Joan||
Publicado en: Commun. Pure Appl. Anal., Edición 16, 2021, ISSN 1534-0392
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2021107

On the limit cycle of a Belousov–Zhabotinsky differential systems

Autores: Jaume Llibre, Regilene Oliveira
Publicado en: Mathematical methods in the applied sciences, 2022, ISSN 1099-1476
Editor: Wiley
DOI: 10.1002/mma.7798

Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points

Autores: Rebiha Benterki, Jaume Llibre
Publicado en: Mathematics, 2020, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math8050755

Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Separated by the Curve y = xn Via Averaging Theory

Autores: Zhifei Guo; Jaume Llibre
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Edición 7, 2022, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127422501875

The limit cycles of a class of piecewise differential systems

Autores: Imane Benabdallah, Rebiha Benterki, Jaume Llibre
Publicado en: Boletín de la Sociedad Matemática Mexicana, Edición 29, 2023, ISSN 1405-213X
Editor: Birkhäuser Verlag
DOI: 10.1007/s40590-023-00535-x

Analysis of a nonlinear financial model

Autores: G Moza, E Grecu, L Tirtirau
Publicado en: Carpathian Journal of Mathematics, Edición 38, 2022, ISSN 1843-4401
Editor: SINUS Association
DOI: 10.37193/cjm.2022.02.17

Analysis of a class of Kolmogorov systems

Autores: G. Tigan, C. Lazureanu, F. Munteanu, C. Sterbeti, A. Florea
Publicado en: Nonlinear Analysis: Real World Applications, Edición 57, 2021, ISSN 1878-5719
Editor: Elsevier
DOI: 10.1016/j.nonrwa.2020.103202

New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree

Autores: Jaume Llibre, Marzieh Mousavi, Arefeh Nabavi
Publicado en: J. Dyn. Control Syst., 2019, ISSN 1079-2724
Editor: Plenum Publishers
DOI: 10.1007/s10883-019-09432-x

Sensor-Based Automated Detection of Electrosurgical Cautery States

Autores: Josh Ehrlich, Amoon Jamzad, Mark Asselin, Jessica Robin Rodgers, Martin Kaufmann,Tamas Haidegger, John Rudan, Parvin Mousavi, Gabor Fichtinger and Tamas Ungi
Publicado en: Sensors, 2022, ISSN 1424-8220
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/s22155808

Global phase portraits of the key pitchfork bifurcation

Autores: Llibre Jaume; Li Shimin
Publicado en: SCIENTIA SINICA Mathematica, Edición 1, 2019, ISSN 2095-9427
Editor: SciEngine
DOI: 10.1360/scm-2018-0266

Centers and limit cycles of vector fields defined on invariant spheres

Autores: C. A. Buzzi, A. L. Rodero, J. Torregrosa
Publicado en: Journal of Nonlinear Science, 2021, ISSN 0938-8974
Editor: Springer Verlag
DOI: 10.1007/s00332-021-09751-z

Integrability by separation of variables

Autores: Jaume Llibre, Rafael Orlando Ramirez
Publicado en: Phys. D, Edición 14, 2020, ISSN 0167-2789
Editor: Elsevier BV
DOI: 10.1016/j.physd.2020.132523

New symmetric periodic solutions for the Maxwell-Bloch differential system

Autores: Murilo R. Cândido, Jaume Llibre, Clàudia Valls
Publicado en: Mathematical Physics, Analysis and Geometry, 2019, ISSN 1385-0172
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11040-019-9313-9

The zero-Hopf bifurcations in the Kolmogorov systems of degree 3 in R3

Autores: Érika Diz-Pita, Jaume Llibre, M. Victoria Otero-Espinar, Claudia Valls
Publicado en: Commun. Nonlinear Sci. Numer. Simul., Edición 12 vols./yr., 2021, ISSN 1007-5704
Editor: Elsevier BV
DOI: 10.1016/j.cnsns.2020.105621

On the indices of singular points for planar bounded piecewise smooth polynomial vector field

Autores: Shimin Li, Jaume Llibre, Xianbo Sun
Publicado en: Nonlinear Anal. Hybrid Syst., 2023, ISSN 1751-570X
Editor: Elsevier BV
DOI: 10.1016/j.nahs.2023.101350

Limit cycles from a monodromic infinity in planar piecewise linear systems

Autores: E. Freire, E. Ponce, J. Torregrosa, F. Torres
Publicado en: Journal of Mathematical Analysis and Applications, 2021, ISSN 1096-0813
Editor: ScienceDirect
DOI: 10.1016/j.jmaa.2020.124818

Periods of holomorphic maps on compact Riemann surfaces and product of spheres

Autores: Llibre, Jaume; Sirvent, Víctor F.
Publicado en: Journal of Difference Equations and Applications, 2020, ISSN 1023-6198
Editor: Taylor & Francis
DOI: 10.1080/10236198.2019.1699915

Invariant algebraic curves of generalized Liénard polynomial differential systems

Autores: Jaume Giné, Jaume Llibre
Publicado en: Mathematics, 2022, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math10020209

A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus

Autores: Florian Munteanu
Publicado en: Symmetry, Edición 21, 2022, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.20944/preprints202207.0291.v1

Global dynamics of a Lotka–Volterra system in ℝ3

Autores: Llibre, J.; Paulina, Martínez; Valls, C.
Publicado en: The Journal of Nonlinear Mathematical Physics, Edición 8, 2020, ISSN 1402-9251
Editor: Luleaa University of Technology
DOI: 10.1080/14029251.2020.1757240

Inflation, Inflation Uncertainty and Fuel Prices in the EU

Autores: ALBULESCU CLAUDIU TIBERIU; STANCU STELIAN; GRECU EUGENIA; TRASCA DANIELA LIVIA
Publicado en: Economic Computation and Economic Cybernetics Studies and Research, Edición 2, 2022, ISSN 0424-267X
Editor: Bucharest University of Economic Studies
DOI: 10.24818/18423264/56.2.22.03

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

Autores: Jaume Llibre, Y. Paulina Martínez
Publicado en: Nonlinear Analysis, Edición 199, 2020, Página(s) 111915, ISSN 0362-546X
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.na.2020.111915

Phase portraits of uniform isochronous centers with homogeneous nonlinearities

Autores: Jaume Llibre, Claudia Valls
Publicado en: J. Dyn. Control Syst., Edición 4 issues/vol./yr., 2021, ISSN 1079-2724
Editor: Plenum Publishers
DOI: 10.1007/s10883-021-09529-2

Bifurcation diagrams in a class of Kolmogorov systems

Autores: G. Tigan, C. Lazureanu, F. Munteanu, C. Sterbeti, A. Florea
Publicado en: Nonlinear Analysis: Real World Applications, Edición 56, 2020, ISSN 1878-5719
Editor: Elsevier
DOI: 10.1016/j.nonrwa.2020.103154

Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field

Autores: Ting Chen; Jaume Llibre
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Edición 10, 2022, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127422501164

Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator

Autores: Rodrigo D Euzébio; Jaume Llibre; Durval J Tonon
Publicado en: Nonlinearity, Edición 10, 2022, ISSN 0951-7715
Editor: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac7691

Qualitative study of a model with Rastall gravity

Autores: Jaume Llibre, Chara Pantazi
Publicado en: Classical and Quantum Gravity, 2020, ISSN 1361-6382
Editor: IOP
DOI: 10.1088/1361-6382/abc188

The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line

Autores: M. Esteban; J. Llibre; C. Valls
Publicado en: Chaos, Edición 15, 2021, ISSN 1054-1500
Editor: American Institute of Physics
DOI: 10.1063/5.0023055

The center problem for the class of Λ-Ω differential systems

Autores: Jaume Llibre, Rafael Ramírez, Valentín Ramírez
Publicado en: Rendiconti del Circolo Matematico di Palermo, 2021, ISSN 0009-725X
Editor: Circolo Matematico di Palermo
DOI: 10.1007/s12215-020-00568-5

Simultaneous bifurcation of limit cycles and critical periods

Autores: R. D. S. Oliveira, I. Sánchez-Sánchez, J. Torregrosa
Publicado en: Qualitative Theory of Dynamical Systems, 2022, ISSN 1575-5460
Editor: Springer Verlag
DOI: 10.1007/s12346-021-00546-x

Hopf bifurcation in 3-dimensional polynomial vector fields

Autores: I. Sánchez-Sánchez, J. Torregrosa
Publicado en: Communications in Nonlinear Science and Numerical Simulation, 2022, ISSN 1007-5704
Editor: Elsevier BV
DOI: 10.1016/j.cnsns.2021.106068

Global dynamics of the integrable Armbruster-Guckenheimer-Kim galactic potential

Autores: J. Llibre, C. Valls
Publicado en: Astrophysics and Space Science, 2019, ISSN 0004-640X
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10509-019-3624-y

First-order perturbation for multi-parameter center families

Autores: J. Itikawa, R. Oliveira, J. Torregrosa
Publicado en: Journal of Differential Equations, 2022, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2021.11.035

A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–Prey System through the KCCGeometric Theory

Autores: F. Munteanu
Publicado en: Symmetry, 2022, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym14091815

Degenerate Chenciner Bifurcation Revisited

Autores: G. Tigan, O. Brandibur, E. A. Kokovics, and L. F. Vesa
Publicado en: International Journal of Bifurcation and Chaos, Edición 31, 2021, ISSN 1793-6551
Editor: World Scientific
DOI: 10.1142/s0218127421501601

New lower bounds of the number of critical periods in reversible centers

Autores: I. Sánchez-Sánchez, J. Torregrosa
Publicado en: Journal of Differential Equations, 2021, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2021.05.013

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

Autores: Maria Elisa Anacleto, Jaume Llibre, Claudia Valls, Claudio Vidal
Publicado en: Nonlinear Analysis: Real World Applications, Edición 60, 2021, Página(s) 103281, ISSN 1468-1218
Editor: Elsevier BV
DOI: 10.1016/j.nonrwa.2020.103281

Zero-Hopf periodic orbits for a Rössler differential system

Autores: Jaume Llibre and Ammar Makhlouf
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2020, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127420501709

Center problem for Λ-Ω differential systems

Autores: Jaume Llibre, Rafael O. Ramírez, Valentín Ramírez
Publicado en: Journal of Differential Equations, 2019, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2019.06.028

Algebraic and topological classification of homogeneous quartic vector fields in the plane

Autores: J. Llibre, Y. P. Martínez, C. Vidal
Publicado en: Annali di Matematica Pura ed Applicata, 2022, ISSN 0373-3114
Editor: Nicola Zanichelli
DOI: 10.1007/s10231-021-01106-5

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

Autores: Jaume Llibre, Regilene D.S. Oliveira, Claudia Valls
Publicado en: Chaos, Solitons & Fractals, Edición 118, 2019, Página(s) 181-186, ISSN 0960-0779
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2018.11.022

Global dynamics of the Buckingham’s two-body problem

Autores: Jaume Llibre, Claudia Valls, Claudio Vidal
Publicado en: Astrophysics and Space Science, Edición 363/12, 2018, Página(s) Article 255, ISSN 0004-640X
Editor: Kluwer Academic Publishers
DOI: 10.1007/s10509-018-3475-y

Invariant Algebraic Surfaces and Hopf Bifurcation of a Finance Model

Autores: Murilo R. Cândido, Jaume Llibre, Claudia Valls
Publicado en: International Journal of Bifurcation and Chaos, Edición 28/12, 2018, Página(s) 1850150, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s021812741850150x

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

Autores: Shimin Li, Jaume Llibre
Publicado en: Chaos, Solitons & Fractals, Edición 120, 2019, Página(s) 149-157, ISSN 0960-0779
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.chaos.2018.12.037

Bounded polynomial vector fields in R 2 and R n

Autores: Luis Barreira, Jaume Llibre, Claudia Valls
Publicado en: Journal of Differential Equations, Edición 268/8, 2020, Página(s) 4416-4422, ISSN 0022-0396
Editor: 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

Autores: Carmen Rocşoreanu, Mihaela Sterpu
Publicado en: International Journal of Bifurcation and Chaos, Edición 29/06, 2019, Página(s) 1950074, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127419500743

Nilpotent Global Centers of Linear Systems with Cubic Homogeneous Nonlinearities

Autores: J. D. García-Saldaña, Jaume Llibre, Claudia Valls
Publicado en: International Journal of Bifurcation and Chaos, Edición 30/01, 2020, Página(s) 2050010, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127420500108

Topological entropy of continuous self-maps on closed surfaces

Autores: Juan Luis García Guirao, Jaume Llibre, Wei Gao
Publicado en: Journal of Difference Equations and Applications, Edición 26/2, 2020, Página(s) 203-208, ISSN 1023-6198
Editor: Taylor & Francis
DOI: 10.1080/10236198.2019.1710141

Limit cycles created by piecewise linear centers

Autores: Jaume Llibre, Xiang Zhang
Publicado en: Chaos: An Interdisciplinary Journal of Nonlinear Science, Edición 29/5, 2019, Página(s) 053116, ISSN 1054-1500
Editor: American Institute of Physics
DOI: 10.1063/1.5086018

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

Autores: Claudio A. Buzzi, Joao C. Medrado, Joan Torregrosa
Publicado en: Journal of Differential Equations, Edición 268/5, 2020, Página(s) 2414-2434, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2019.09.008

Bifurcations from families of periodic solutions in piecewise differential systems

Autores: Jaume Llibre, Douglas D. Novaes, Camila A.B. Rodrigues
Publicado en: Physica D: Nonlinear Phenomena, Edición 404, 2020, Página(s) 132342, ISSN 0167-2789
Editor: Elsevier BV
DOI: 10.1016/j.physd.2020.132342

Limit cycles for two classes of control piecewise linear differential systems

Autores: Jaume Llibre, Regilene D. Oliveira, Camila Ap. B. Rodrigues
Publicado en: São Paulo Journal of Mathematical Sciences, Edición 36, 2020, Página(s) 1-17, ISSN 1982-6907
Editor: Springer
DOI: 10.1007/s40863-020-00163-7

Stability and bifurcation analysis of a four-dimensional economic model

Autores: G Moza, C Rocşoreanu, M Sterpu, R Oliveira
Publicado en: Carpathian Journal of Mathematics, Edición 40, 2024, ISSN 1843-4401
Editor: SINUS Association
DOI: 10.37193/cjm.2024.01.10

A survey on the Kovalevskaya exponents and their applications

Autores: Jaume Llibre, Yuzhou Tian
Publicado en: Journal of mathematical analysis and applications, 2021, ISSN 0022-247X
Editor: Academic Press
DOI: 10.1016/j.jmaa.2021.125576

Another Case of Degenerated Discrete Chenciner Dynamic System and Economics

Autores: Sorin Lugojan; Loredana Ciurdariu; Eugenia Grecu
Publicado en: Mathematics, Edición 16, 2022, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math10203782

Nonexistence and Uniqueness of Limit Cycles in a Class of Three-Dimensional Piecewise Linear Differential Systems

Autores: Ting Chen; Lihong Huang; Jaume Llibre
Publicado en: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Edición 5, 2023, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s021812742350075x

Analysis of Degenerate Chenciner Bifurcation

Autores: G. Tigan, S. Lugojan, and L. Ciurdariu
Publicado en: International Journal of Bifurcation and Chaos, Edición 30, 2020, ISSN 1793-6551
Editor: World Scientific
DOI: 10.1142/s0218127420502454

Z2-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields

Autores: Ting Chen, Shimin Li, Jaume Llibre
Publicado en: J. Differential Equations, 2020, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2019.12.020

Zero-Hopf bifurcation in the Chua's circuit

Autores: J-M. Ginoux, J. Llibre
Publicado en: Journal of Mathematical Physics, 2023, ISSN 0022-2488
Editor: American Institute of Physics
DOI: 10.1063/5.0137020

The Limit Cycles of Discontinuous Piecewise Linear Differential Systems Formed by Centers and Separated by Irreducible Cubic Curves II

Autores: Rebiha Benterki; Loubna Damene; Jaume Llibre
Publicado en: Differ. Equ. Dyn. Syst., Edición 16, 2021, ISSN 0971-3514
Editor: Research Square Publications
DOI: 10.1007/s12591-021-00564-w

On the Bifurcations of a 3D Symmetric Dynamical System

Autores: Dana Constantinescu
Publicado en: Symmetry, Edición 9, 2023, ISSN 2073-8994
Editor: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym15040923

Invariants of polynomial vector fields

Autores: J. Llibre, C. Valls
Publicado en: Journal of Differential Equations, 2023, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2023.05.024

Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line

Autores: Jaume Llibre
Publicado en: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, ISSN 1024-7696
Editor: Publishing and Printing State Enterprise Stiinta

Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary

Autores: Tao Li; Jaume Llibre
Publicado en: Physica D. Nonlinear phenomena, Edición 15, 2021, ISSN 0167-2789
Editor: Elsevier BV
DOI: 10.1016/j.physd.2021.132855

Transcritical bifurcation at infinity in planar piecewise polynomial differential systems with two zones

Autores: Denis de Carvalho Braga, Jaume Llibre, Luis Fernando Mello
Publicado en: Dynamical Systems. An International Journal, Edición 4 issues/vol./yr., 2022, ISSN 1468-9367
Editor: Taylor & Francis
DOI: 10.1080/14689367.2022.2092454

On topological entropy, Lefschetz numbers and Lefschetz zeta functions

Autores: Jaume Llibre, Victor F. Sirvent
Publicado en: General Topology and Appl., Edición 4 issues/vol./yr., 2019, ISSN 0016-660X
Editor: North-Holland
DOI: 10.1016/j.topol.2019.106906

Output, Uncertainty and Fuel Prices in the EU Countries

Autores: Pârtachi Ion Profir; Grecu Eugenia; Albulescu Claudiu Tiberiu; Stancu Stelian; Trasca Daniela Livia
Publicado en: Economic Computation and Economic Cybernetics Studies and Research, Edición 4, 2020, ISSN 0424-267X
Editor: Instrumentul Bibliometric National
DOI: 10.24818/18423264/54.1.20.02

Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve

Autores: Jeidy J. Jimenez, Jaume Llibre, Joao Carlos Medrado
Publicado en: Electron. J. Qual. Theory Differ. Equ., 2020, ISSN 1417-3875
Editor: Szegedi Tudomanyegyetern/University of Szeged
DOI: 10.14232/ejqtde.2020.1.19

Z2-symmetric planar polynomial Hamiltonian systems of degree 3 with nilpotent centers

Autores: Fabio Scalco Dias, Jaume Llibre, Clàudia Valls
Publicado en: Electron. J. Differential Equations, 2019, ISSN 1072-6691
Editor: Texas State University - San Marcos

The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve $$y=x^{n}$$

Autores: Jaume Llibre, Claudia Valls
Publicado en: Mathematical Physics, Analysis and Geometry, Edición 26, 2023, ISSN 1385-0172
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11040-023-09467-4

Global centers of a family of cubic systems

Autores: Appis, Raul Felipe; Llibre, Jaume
Publicado en: Aequationes mathematicae, Edición 1, 2024, ISSN 0001-9054
Editor: Birkhauser Verlag
DOI: 10.1007/s00010-024-01051-7

Global Dynamics of the Hořava–Lifshitz Cosmological Model in a Non-Flat Universe with Non-Zero Cosmological Constant

Autores: Fabao Gao; Jaume Llibre
Publicado en: Universe, Edición 14, 2021, ISSN 2218-1997
Editor: MDPI
DOI: 10.3390/universe7110445

Limit cycles of piecewise polynomial differential systems with the discontinuity line xy = 0

Autores: Tao Li, Jaume Llibre
Publicado en: Commun. Pure Appl. Anal., Edición 12 issues/vol./yr., 2021, ISSN 1534-0392
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2021136

Periodic Orbits of Quantised Restricted Three-Body Problem

Autores: Elbaz I. Abouelmagd, Juan Luis Garcia Guirao, Jaume Llibre
Publicado en: Universe, 2023, ISSN 2218-1997
Editor: Universe
DOI: 10.3390/universe9030149

Periods of Morse–Smale diffeomorphisms on S^n, S^m×S^n, CP^n and HP^n

Autores: C. Cufi-Cabre, J. Llibre
Publicado en: Journal of Fixed Point Theory and Applications, 2022, ISSN 1661-7746
Editor: Birkhauser Verlag
DOI: 10.1007/s11784-021-00918-5

The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems

Autores: Rebiha Benterki, Jaume Llibre
Publicado en: Nonlinear Dynam., Edición 16 issues/4 vols./yr., 2020, ISSN 0924-090X
Editor: Kluwer Academic Publishers
DOI: 10.1007/s11071-020-06045-z

Chenciner Bifurcation Presenting a Further Degree of Degeneration

Autores: Sorin Lugojan; Loredana Ciurdariu; Eugenia Grecu
Publicado en: Mathematics, Edición 26, 2022, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math10091603

Nilpotent Bicenters in Continuous Piecewise Z2-Equivariant Cubic Polynomial Hamiltonian Vector Fields: Cusp–Cusp Type

Autores: Ting Chen and Jaume Llibre
Publicado en: International Journal of Bifurcation and Chaos, 2023, ISSN 0218-1274
Editor: World Scientific Publishing Co
DOI: 10.1142/s0218127423501389

The Classical and Improved Euler-Jacobi Formula and Polynomial Vector Fields in Rn

Autores: Jaume Llibre, Claudia Valls
Publicado en: Journal of dynamics and differential equations, 2022, ISSN 1040-7294
Editor: Plenum Publishers
DOI: 10.1007/s10884-022-10191-w

Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces

Autores: Jaume Llibre, Yuzhou Tian
Publicado en: Zeitschrift fur Angewandte Mathematik und Physik, 2021, ISSN 0044-2275
Editor: Birkhauser Verlag
DOI: 10.1007/s00033-020-01450-1

Criteria on the existence of limit cycles in planar polynomial differential systems

Autores: Jaume Giné; Maite Grau; Jaume Llibre
Publicado en: Expositiones Mathematicae, Edición 7, 2022, ISSN 0723-0869
Editor: Elsevier BV
DOI: 10.1016/j.exmath.2022.09.002

Crossing limit cycles for a class of piecewise linear differential centers separated by a conic

Autores: JOHANA JIMENEZ, JAUME LLIBRE, JOAO C. MEDRADO
Publicado en: Electronic Journal of Differential Equations, 2020, ISSN 1072-6691
Editor: Texas State University - San Marcos

Analysis of interactions between human immune system and a pathogenic virus

Autores: G Moza, LV Vesa
Publicado en: Carpathian Journal of Mathematics, Edición 39, 2023, ISSN 1843-4401
Editor: SINUS Association
DOI: 10.37193/cjm.2023.02.06

Periodic structure of transversal maps on sum-free products of spheres

Autores: Jaume Llibre, Víctor F. Sirvent
Publicado en: J. Difference Equ. Appl., 2019, ISSN 1023-6198
Editor: Taylor & Francis
DOI: 10.1080/10236198.2019.1606216

Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system

Autores: Constantinescu, Dana; Tigan, Gheorghe; Zhang, Xiang
Publicado en: Open Research Europe, Edición 41, 2021, ISSN 2732-5121
Editor: European Commission
DOI: 10.12688/openreseurope.13590.1

Non-equivalence between the Melnikov and the averaging methods for nonsmooth differential systems

Autores: Zhifei Guo, Jaume Llibre
Publicado en: Qual. Theory Dyn. Syst., 2022, ISSN 1575-5460
Editor: Springer Verlag
DOI: 10.1007/s12346-022-00643-5

The limit cycles of the Higgins-Selkov systems

Autores: Hebai Chen, Jaume Llibre, Yilei Tang
Publicado en: J. Nonlinear Sci., Edición 6 issues/vol./yr., 2021, ISSN 0938-8974
Editor: Springer Verlag
DOI: 10.1007/s00332-021-09742-0

Non-existence and uniqueness of limit cycles in a class of generalized Liénard equations

Autores: J. Llibre, C. Valls
Publicado en: Boletín de la Sociedad Matemática Mexicana, 2022, ISSN 2296-4495
Editor: Birkhauser
DOI: 10.1007/s40590-022-00433-8

On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3

Autores: Maoan Han, Jaume Llibre, Yun Tian
Publicado en: Mathematics, 2020, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math8071137

The Markus-Yamabe conjecture for continuous and discontinuous piecewise linear differential systems

Autores: J. Llibre, X. Zhang
Publicado en: Proceedings of the American Mathematical Society, 2021, ISSN 1088-6826
Editor: American Mathematical Society
DOI: 10.1090/proc/15601

The study of the singular bifurcation of a 3D dynamical system of interest in ecology

Autores: D. Constantinescu
Publicado en: Edición 49, 2022, ISSN 2271-2097
Editor: ITM Web of Conferences
DOI: 10.1051/itmconf/20224902002

The behaviour of an epidemiological model, , 01002 (2022).

Autores: L. Bucur
Publicado en: 2022, ISSN 2271-2097
Editor: ITM Web of Conferences
DOI: 10.1051/itmconf/20224901002

A mathematical model of infectious disease transmission

Autores: Florea Aurelia; Lăzureanu Cristian
Publicado en: ITM Web of Conferences, Edición 62, 2020, ISSN 2271-2097
Editor: EDP Sciences
DOI: 10.1051/itmconf/20203402002

A study of a three-dimensional competitive Lotka–Volterra system

Autores: Munteanu Florian
Publicado en: ITM Web of Conferences, Vol 34, p 03010 (2020), Edición 55, 2020, ISSN 2271-2097
Editor: EDP Sciences
DOI: 10.1051/itmconf/20203403010

The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach

Autores: Danet Cristian Paul
Publicado en: ITM Web of Conferences, Edición 34, 2020, ISSN 2271-2097
Editor: EDP Sciences
DOI: 10.1051/itmconf/20203403005

3D Quadratic ODE systems with an infinite number of limit cycles

Autores: E. Musafirov, A. Grin, A. Pranevich, F. Munteanu, C. Sterbeti
Publicado en: ITM Web of Conferences, 2022, ISSN 2271-2097
Editor: edpsciences
DOI: 10.1051/itmconf/20224902006

A Spray Theory for the Geometric Method in Hydrodynamics

Autores: Cismas, Emanuel Ciprian
Publicado en: Edición 33, 2019
Editor: arxiv
DOI: 10.48550/arxiv.1909.13483

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