Contributions to codimension k bifurcations in dynamical systems theory

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Deliverables

First press article

The deliverable will contain the whole article and details of the means where it was published.

Second and third press articles

The deliverable will contain the whole articles and details of the means where they were published.

The project website

This deliverable will contain a text with the link to the project website.

Publications

A Bendixon–Dulac theorem for some piecewise systems

Author(s): Leonardo P C da Cruz; Joan Torregrosa
Published in: Nonlinearity, 2020, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab6812

Analysis of a map-based neuronal model

Author(s): G. Tigan, R. Efrem
Published in: Journal of Difference Equations and Applications, 2020, ISSN 1563-5120
Publisher: Taylor & Francis
DOI: 10.1080/10236198.2020.1780219

On the Jacobi Stability of Two SIR Epidemic Patterns With Demography

Author(s): Florian Munteanu
Published in: Symmetry, Issue 9, 2023, ISSN 2073-8994
Publisher: 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

Author(s): Jaume Llibre; Fabao Gao; Fabao Gao
Published in: Eur. Phys. J. C Part. Fields, 2020, ISSN 1434-6044
Publisher: Springer Verlag
DOI: 10.1140/epjc/s10052-020-7714-3

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

Author(s): Jean-Marc Ginoux; Jaume Llibre; Claudia Valls
Published in: Math. Phys. Anal. Geom., Issue 16, 2021, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-020-09372-0

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

Author(s): Jaume Llibre; Regilene D. S. Oliveira; Camila A. B. Rodrigues
Published in: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, ISSN 1072-6691
Publisher: 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

Author(s): Louiza Baymout, Rebiha Benterki, Jaume Llibre
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2023, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127423501663

Phase portraits of two classes of Liénard equations

Author(s): Jie Li, Jaume Llibre
Published in: Boletin de la Sociedad Matematica Mexicana, 2023, ISSN 1405-213X
Publisher: Birkhäuser Verlag
DOI: 10.1007/s40590-022-00479-8

Phase portraits of an SIR epidemic model

Author(s): Jaume Llibre, Tayeb Salhi
Published in: Applicable Analysis. An International Journal, 2024, ISSN 0003-6811
Publisher: Taylor & Francis
DOI: 10.1080/00036811.2023.2235390

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

Author(s): Jaume Llibre, Pengfei Yuan
Published in: Qual. Theory Dyn. Syst., 2019, ISSN 1575-5460
Publisher: Springer Verlag
DOI: 10.1007/s12346-019-00322-y

Limit cycles on piecewise smooth vector fields with coupled rigid centers

Author(s): Tiago Carvalho, Luiz Fernando Gonçalves, Jaume Llibre
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Issue 16 issues/vol./yr., 2021, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127421502242

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

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

Author(s): C. Ionescu, C. N. Babalic, R. Constantinescu, R. Efrem
Published in: Symmetry, 2022, ISSN 2073-8994
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym14040827

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

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

Author(s): Jaume Llibre, Xiang Zhang
Published in: Expositiones Mathematicae, 2021, ISSN 0723-0869
Publisher: 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

Author(s): M. E. Anacleto, J. Llibre, C. Valls, C. Vidal
Published in: Boletín de la Sociedad Matemática Mexicana, 2023, ISSN 2296-4495
Publisher: Springer
DOI: 10.1007/s40590-023-00501-7

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

Author(s): Meriem Barkat, Rebiha Benterki, Jaume Llibre
Published in: Nonlinear Dynam., 2023, ISSN 0924-090X
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11071-022-07891-9

Analyzing the Jacobi Stability of Lü’s Circuit System

Author(s): Munteanu, Florian
Published in: Symmetry, Issue 23, 2022, ISSN 2073-8994
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym14061248

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

Author(s): Georgeta Soava; Anca Mehedintu; Mihaela Sterpu; Eugenia Grecu
Published in: Energies, 2021, ISSN 1996-1073
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/en14092394

Polynomial Liénard systems with a nilpotent global center

Author(s): Isaac A. García; Jaume Llibre
Published in: Rendiconti del Circolo Matematico di Palermo Series 2, Issue 6, 2023, ISSN 0009-725X
Publisher: Circolo Matematico di Palermo
DOI: 10.1007/s12215-022-00850-8

Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems

Author(s): Jie Li; Jaume Llibre
Published in: Differ. Equ. Dyn. Syst., Issue 1, 2023, ISSN 0971-3514
Publisher: Research Square Publications
DOI: 10.1007/s12591-023-00666-7

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

Author(s): L. P. C. da Cruz, J. Torregrosa, , Journal of Mathematical Analysis and Applications, 514 (2022) 126256.
Published in: Journal of Mathematical Analysis and Applications, Issue 514, 2022, ISSN 1096-0813
Publisher: Elsevier
DOI: 10.1016/j.jmaa.2022.126256

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

Author(s): M. Esteban, J. Llibre, C. Valls
Published in: International Journal of Bifurcation and Chaos, 2021, ISSN 0218-1274
Publisher: 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

Author(s): Florian Munteanu
Published in: https://www.preprints.org/manuscript/202208.0129/v1, Issue 19, 2022, ISSN 2073-8994
Publisher: 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

Author(s): Denis de Carvalho Braga, Fabio Scalco Dias, Jaume Llibre, Luis Fernando Mello
Published in: São Paulo Journal of Mathematical Sciences, 2023, ISSN 1982-6907
Publisher: Springer
DOI: 10.1007/s40863-023-00368-6

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

Author(s): Jaume Llibre; Arefeh Nabavi; Marzieh Mousavi
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Issue 19, 2020, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127420500510

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

Author(s): Jaume Llibre, Yuzhou Tian
Published in: Discrete Contin. Dyn. Syst. Ser. B, Issue 12 issues/vol./yr., 2021, ISSN 1531-3492
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcdsb.2021228

Applied higher-order elliptic problems with nonstandard growth structure

Author(s): Maria-Magdalena Boureanu, Alejandro Vélez-Santiago
Published in: Applied Mathematics Letters, 2022, ISSN 0893-9659
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.aml.2021.107603

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

Author(s): X. Chen, T. Li, J. Llibre
Published in: Journal of Differential Equations, 2022, ISSN 1090-2732
Publisher: Elsevier
DOI: 10.1016/j.jde.2022.01.019

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

Author(s): Belén García, JaumeLlibre, Antón Lombardero, Jesús Suárez Pérez del Río
Published in: J. Symbolic Comput., 2019, ISSN 0747-7171
Publisher: Academic Press
DOI: 10.1016/j.jsc.2018.08.006

Existence and uniqueness for a semilinear sixth-order

Author(s): C-P. Danet
Published in: Electronic Journal of Qualitative Theory of Differential Equations, 2022, ISSN 1417-3875
Publisher: 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

Author(s): Jean-Marc Ginoux, Jaume Llibre
Published in: J. Geom. Phys., Issue 12 vols./yr., 2023, ISSN 0393-0440
Publisher: 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

Author(s): Ali Bakhshalizadeh, Jaume Llibre
Published in: Differential Equations and Dynamical Systems, 2024, ISSN 0971-3514
Publisher: Research Square Publications
DOI: 10.1007/s12591-022-00597-9

Phase Portraits of the Leslie-Gower System

Author(s): Llibre, Jaume||; Valls, Clàudia||
Published in: Acta Mathematica Scientia, Issue 9, 2022, ISSN 0252-9602
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10473-022-0502-4

Analysis of a Class of Lotka–Volterra Systems

Author(s): G Moza, D Constantinescu, R Efrem, L Bucur, R Constantinescu
Published in: Qualitative theory of dynamical systems, Issue 21, 2022, ISSN 1662-3592
Publisher: Springer
DOI: 10.1007/s12346-022-00563-4

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

Dynamics of a Generalized Rayleigh System

Author(s): Maíra Duran Baldissera, Jaume Llibre, Regilene Oliveira
Published in: Differential Equations and Dynamical Systems,, 2024, ISSN 0971-3514
Publisher: Research Square Publications
DOI: 10.1007/s12591-022-00604-z

Phase Portraits of Families VII and VIII of the Quadratic Systems

Author(s): Laurent Cairó; Jaume Llibre
Published in: Axioms, Issue 3, 2023, ISSN 2075-1680
Publisher: MDPI
DOI: 10.3390/axioms12080756

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

Author(s): Jaume Llibre, Yuzhou Tian
Published in: Acta Appl. Math., Issue 6 vols./yr, 2021, ISSN 0167-8019
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10440-021-00407-4

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

Author(s): Ting Chen, Jaume Llibre
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2018, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127418501687

Admissible Perturbations of a Generalized Langford System

Author(s): Eduard Musafirov; Alexander Grin; Andrei Pranevich
Published in: International Journal of Bifurcation and Chaos, 2022, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127422500389

Periodic solutions of a class of Duffing differential equations

Author(s): Rebiha Benterki, Jaume Llibre
Published in: Journal of Nonlinear Modeling and Analysis, 2019, ISSN 2562-2854
Publisher: Zhejiang Normal University
DOI: 10.12150/jnma.2019.167

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

Author(s): Renáta Nagyné Elek; Tamás Haidegger
Published in: Journal of Clinical Medicine, Issue 6, 2022, ISSN 2077-0383
Publisher: 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

Author(s): Florian Munteanu; Alexander Grin; Eduard Musafirov; Andrei Pranevich; Cătălin Şterbeţi
Published in: Symmetry, Issue 10, 2023, ISSN 2073-8994
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym15030598

LIMIT CYCLES OF THE DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS ON THE CYLINDER

Author(s): Li, Jie; Llibre, Jaume||
Published in: J. Appl. Anal. Comput., Issue 11, 2022, ISSN 2156-907X
Publisher: Wilmington Sci. Publ. Shanghai Norm. Univ.
DOI: 10.11948/20220031

An analysis of two degenerate double-Hopf bifurcations

Author(s): Gheorghe Moza, Mihaela Sterpu , Carmen Rocşoreanu
Published in: Electronic Research Archive, Issue 30, 2022, ISSN 2688-1594
Publisher: AIMS Press
DOI: 10.3934/era.2022020

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

Author(s): J. Llibre, V.F. Sirvent
Published in: Computational and Applied Mathematics, 2021, ISSN 1807-0302
Publisher: Springer
DOI: 10.1007/s40314-021-01677-2

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

Dynamics of a four-dimensional economic model

Author(s): G Moza, O Brandibur, A Găină
Published in: Mathematics, Issue 11, 2023, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math11040797

Orbitally symmetric systems with applications to planar centers

Author(s): Bastos, Jefferson L. R.||; Buzzi, Claudio||; Torregrosa, Joan||
Published in: Commun. Pure Appl. Anal., Issue 16, 2021, ISSN 1534-0392
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2021107

On the limit cycle of a Belousov–Zhabotinsky differential systems

Author(s): Jaume Llibre, Regilene Oliveira
Published in: Mathematical methods in the applied sciences, 2022, ISSN 1099-1476
Publisher: Wiley
DOI: 10.1002/mma.7798

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

Author(s): Rebiha Benterki, Jaume Llibre
Published in: Mathematics, 2020, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math8050755

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

Author(s): Zhifei Guo; Jaume Llibre
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Issue 7, 2022, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127422501875

The limit cycles of a class of piecewise differential systems

Author(s): Imane Benabdallah, Rebiha Benterki, Jaume Llibre
Published in: Boletín de la Sociedad Matemática Mexicana, Issue 29, 2023, ISSN 1405-213X
Publisher: Birkhäuser Verlag
DOI: 10.1007/s40590-023-00535-x

Analysis of a nonlinear financial model

Author(s): G Moza, E Grecu, L Tirtirau
Published in: Carpathian Journal of Mathematics, Issue 38, 2022, ISSN 1843-4401
Publisher: SINUS Association
DOI: 10.37193/cjm.2022.02.17

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

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

Author(s): Jaume Llibre, Marzieh Mousavi, Arefeh Nabavi
Published in: J. Dyn. Control Syst., 2019, ISSN 1079-2724
Publisher: Plenum Publishers
DOI: 10.1007/s10883-019-09432-x

Sensor-Based Automated Detection of Electrosurgical Cautery States

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

Global phase portraits of the key pitchfork bifurcation

Author(s): Llibre Jaume; Li Shimin
Published in: SCIENTIA SINICA Mathematica, Issue 1, 2019, ISSN 2095-9427
Publisher: SciEngine
DOI: 10.1360/scm-2018-0266

Centers and limit cycles of vector fields defined on invariant spheres

Author(s): C. A. Buzzi, A. L. Rodero, J. Torregrosa
Published in: Journal of Nonlinear Science, 2021, ISSN 0938-8974
Publisher: Springer Verlag
DOI: 10.1007/s00332-021-09751-z

Integrability by separation of variables

Author(s): Jaume Llibre, Rafael Orlando Ramirez
Published in: Phys. D, Issue 14, 2020, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2020.132523

New symmetric periodic solutions for the Maxwell-Bloch differential system

Author(s): Murilo R. Cândido, Jaume Llibre, Clàudia Valls
Published in: Mathematical Physics, Analysis and Geometry, 2019, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-019-9313-9

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

Author(s): Érika Diz-Pita, Jaume Llibre, M. Victoria Otero-Espinar, Claudia Valls
Published in: Commun. Nonlinear Sci. Numer. Simul., Issue 12 vols./yr., 2021, ISSN 1007-5704
Publisher: Elsevier BV
DOI: 10.1016/j.cnsns.2020.105621

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

Author(s): Shimin Li, Jaume Llibre, Xianbo Sun
Published in: Nonlinear Anal. Hybrid Syst., 2023, ISSN 1751-570X
Publisher: Elsevier BV
DOI: 10.1016/j.nahs.2023.101350

Limit cycles from a monodromic infinity in planar piecewise linear systems

Author(s): E. Freire, E. Ponce, J. Torregrosa, F. Torres
Published in: Journal of Mathematical Analysis and Applications, 2021, ISSN 1096-0813
Publisher: ScienceDirect
DOI: 10.1016/j.jmaa.2020.124818

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

Author(s): Llibre, Jaume; Sirvent, Víctor F.
Published in: Journal of Difference Equations and Applications, 2020, ISSN 1023-6198
Publisher: Taylor & Francis
DOI: 10.1080/10236198.2019.1699915

Invariant algebraic curves of generalized Liénard polynomial differential systems

Author(s): Jaume Giné, Jaume Llibre
Published in: Mathematics, 2022, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math10020209

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

Author(s): Florian Munteanu
Published in: Symmetry, Issue 21, 2022, ISSN 2073-8994
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.20944/preprints202207.0291.v1

Global dynamics of a Lotka–Volterra system in ℝ3

Author(s): Llibre, J.; Paulina, Martínez; Valls, C.
Published in: The Journal of Nonlinear Mathematical Physics, Issue 8, 2020, ISSN 1402-9251
Publisher: Luleaa University of Technology
DOI: 10.1080/14029251.2020.1757240

Inflation, Inflation Uncertainty and Fuel Prices in the EU

Author(s): ALBULESCU CLAUDIU TIBERIU; STANCU STELIAN; GRECU EUGENIA; TRASCA DANIELA LIVIA
Published in: Economic Computation and Economic Cybernetics Studies and Research, Issue 2, 2022, ISSN 0424-267X
Publisher: Bucharest University of Economic Studies
DOI: 10.24818/18423264/56.2.22.03

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

Phase portraits of uniform isochronous centers with homogeneous nonlinearities

Author(s): Jaume Llibre, Claudia Valls
Published in: J. Dyn. Control Syst., Issue 4 issues/vol./yr., 2021, ISSN 1079-2724
Publisher: Plenum Publishers
DOI: 10.1007/s10883-021-09529-2

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

Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field

Author(s): Ting Chen; Jaume Llibre
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Issue 10, 2022, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127422501164

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

Author(s): Rodrigo D Euzébio; Jaume Llibre; Durval J Tonon
Published in: Nonlinearity, Issue 10, 2022, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac7691

Qualitative study of a model with Rastall gravity

Author(s): Jaume Llibre, Chara Pantazi
Published in: Classical and Quantum Gravity, 2020, ISSN 1361-6382
Publisher: 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

Author(s): M. Esteban; J. Llibre; C. Valls
Published in: Chaos, Issue 15, 2021, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0023055

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

Author(s): Jaume Llibre, Rafael Ramírez, Valentín Ramírez
Published in: Rendiconti del Circolo Matematico di Palermo, 2021, ISSN 0009-725X
Publisher: Circolo Matematico di Palermo
DOI: 10.1007/s12215-020-00568-5

Simultaneous bifurcation of limit cycles and critical periods

Author(s): R. D. S. Oliveira, I. Sánchez-Sánchez, J. Torregrosa
Published in: Qualitative Theory of Dynamical Systems, 2022, ISSN 1575-5460
Publisher: Springer Verlag
DOI: 10.1007/s12346-021-00546-x

Hopf bifurcation in 3-dimensional polynomial vector fields

Author(s): I. Sánchez-Sánchez, J. Torregrosa
Published in: Communications in Nonlinear Science and Numerical Simulation, 2022, ISSN 1007-5704
Publisher: Elsevier BV
DOI: 10.1016/j.cnsns.2021.106068

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

Author(s): J. Llibre, C. Valls
Published in: Astrophysics and Space Science, 2019, ISSN 0004-640X
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10509-019-3624-y

First-order perturbation for multi-parameter center families

Author(s): J. Itikawa, R. Oliveira, J. Torregrosa
Published in: Journal of Differential Equations, 2022, ISSN 0022-0396
Publisher: 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

Author(s): F. Munteanu
Published in: Symmetry, 2022, ISSN 2073-8994
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym14091815

Degenerate Chenciner Bifurcation Revisited

Author(s): G. Tigan, O. Brandibur, E. A. Kokovics, and L. F. Vesa
Published in: International Journal of Bifurcation and Chaos, Issue 31, 2021, ISSN 1793-6551
Publisher: World Scientific
DOI: 10.1142/s0218127421501601

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

Author(s): I. Sánchez-Sánchez, J. Torregrosa
Published in: Journal of Differential Equations, 2021, ISSN 0022-0396
Publisher: 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

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

Zero-Hopf periodic orbits for a Rössler differential system

Author(s): Jaume Llibre and Ammar Makhlouf
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2020, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127420501709

Center problem for Λ-Ω differential systems

Author(s): Jaume Llibre, Rafael O. Ramírez, Valentín Ramírez
Published in: Journal of Differential Equations, 2019, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.06.028

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

Author(s): J. Llibre, Y. P. Martínez, C. Vidal
Published in: Annali di Matematica Pura ed Applicata, 2022, ISSN 0373-3114
Publisher: Nicola Zanichelli
DOI: 10.1007/s10231-021-01106-5

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

Stability and bifurcation analysis of a four-dimensional economic model

Author(s): G Moza, C Rocşoreanu, M Sterpu, R Oliveira
Published in: Carpathian Journal of Mathematics, Issue 40, 2024, ISSN 1843-4401
Publisher: SINUS Association
DOI: 10.37193/cjm.2024.01.10

A survey on the Kovalevskaya exponents and their applications

Author(s): Jaume Llibre, Yuzhou Tian
Published in: Journal of mathematical analysis and applications, 2021, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.1016/j.jmaa.2021.125576

Another Case of Degenerated Discrete Chenciner Dynamic System and Economics

Author(s): Sorin Lugojan; Loredana Ciurdariu; Eugenia Grecu
Published in: Mathematics, Issue 16, 2022, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math10203782

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

Author(s): Ting Chen; Lihong Huang; Jaume Llibre
Published in: Internat. J. Bifur. Chaos Appl. Sci. Engrg., Issue 5, 2023, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s021812742350075x

Analysis of Degenerate Chenciner Bifurcation

Author(s): G. Tigan, S. Lugojan, and L. Ciurdariu
Published in: International Journal of Bifurcation and Chaos, Issue 30, 2020, ISSN 1793-6551
Publisher: World Scientific
DOI: 10.1142/s0218127420502454

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

Author(s): Ting Chen, Shimin Li, Jaume Llibre
Published in: J. Differential Equations, 2020, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.12.020

Zero-Hopf bifurcation in the Chua's circuit

Author(s): J-M. Ginoux, J. Llibre
Published in: Journal of Mathematical Physics, 2023, ISSN 0022-2488
Publisher: 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

Author(s): Rebiha Benterki; Loubna Damene; Jaume Llibre
Published in: Differ. Equ. Dyn. Syst., Issue 16, 2021, ISSN 0971-3514
Publisher: Research Square Publications
DOI: 10.1007/s12591-021-00564-w

On the Bifurcations of a 3D Symmetric Dynamical System

Author(s): Dana Constantinescu
Published in: Symmetry, Issue 9, 2023, ISSN 2073-8994
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/sym15040923

Invariants of polynomial vector fields

Author(s): J. Llibre, C. Valls
Published in: Journal of Differential Equations, 2023, ISSN 0022-0396
Publisher: 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

Author(s): Jaume Llibre
Published in: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, ISSN 1024-7696
Publisher: Publishing and Printing State Enterprise Stiinta

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

Author(s): Tao Li; Jaume Llibre
Published in: Physica D. Nonlinear phenomena, Issue 15, 2021, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2021.132855

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

Author(s): Denis de Carvalho Braga, Jaume Llibre, Luis Fernando Mello
Published in: Dynamical Systems. An International Journal, Issue 4 issues/vol./yr., 2022, ISSN 1468-9367
Publisher: Taylor & Francis
DOI: 10.1080/14689367.2022.2092454

On topological entropy, Lefschetz numbers and Lefschetz zeta functions

Author(s): Jaume Llibre, Victor F. Sirvent
Published in: General Topology and Appl., Issue 4 issues/vol./yr., 2019, ISSN 0016-660X
Publisher: North-Holland
DOI: 10.1016/j.topol.2019.106906

Output, Uncertainty and Fuel Prices in the EU Countries

Author(s): Pârtachi Ion Profir; Grecu Eugenia; Albulescu Claudiu Tiberiu; Stancu Stelian; Trasca Daniela Livia
Published in: Economic Computation and Economic Cybernetics Studies and Research, Issue 4, 2020, ISSN 0424-267X
Publisher: 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

Author(s): Jeidy J. Jimenez, Jaume Llibre, Joao Carlos Medrado
Published in: Electron. J. Qual. Theory Differ. Equ., 2020, ISSN 1417-3875
Publisher: Szegedi Tudomanyegyetern/University of Szeged
DOI: 10.14232/ejqtde.2020.1.19

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

Author(s): Fabio Scalco Dias, Jaume Llibre, Clàudia Valls
Published in: Electron. J. Differential Equations, 2019, ISSN 1072-6691
Publisher: Texas State University - San Marcos

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

Author(s): Jaume Llibre, Claudia Valls
Published in: Mathematical Physics, Analysis and Geometry, Issue 26, 2023, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-023-09467-4

Global centers of a family of cubic systems

Author(s): Appis, Raul Felipe; Llibre, Jaume
Published in: Aequationes mathematicae, Issue 1, 2024, ISSN 0001-9054
Publisher: 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

Author(s): Fabao Gao; Jaume Llibre
Published in: Universe, Issue 14, 2021, ISSN 2218-1997
Publisher: MDPI
DOI: 10.3390/universe7110445

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

Author(s): Tao Li, Jaume Llibre
Published in: Commun. Pure Appl. Anal., Issue 12 issues/vol./yr., 2021, ISSN 1534-0392
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2021136

Periodic Orbits of Quantised Restricted Three-Body Problem

Author(s): Elbaz I. Abouelmagd, Juan Luis Garcia Guirao, Jaume Llibre
Published in: Universe, 2023, ISSN 2218-1997
Publisher: Universe
DOI: 10.3390/universe9030149

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

Author(s): C. Cufi-Cabre, J. Llibre
Published in: Journal of Fixed Point Theory and Applications, 2022, ISSN 1661-7746
Publisher: 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

Author(s): Rebiha Benterki, Jaume Llibre
Published in: Nonlinear Dynam., Issue 16 issues/4 vols./yr., 2020, ISSN 0924-090X
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11071-020-06045-z

Chenciner Bifurcation Presenting a Further Degree of Degeneration

Author(s): Sorin Lugojan; Loredana Ciurdariu; Eugenia Grecu
Published in: Mathematics, Issue 26, 2022, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math10091603

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

Author(s): Ting Chen and Jaume Llibre
Published in: International Journal of Bifurcation and Chaos, 2023, ISSN 0218-1274
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218127423501389

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

Author(s): Jaume Llibre, Claudia Valls
Published in: Journal of dynamics and differential equations, 2022, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-022-10191-w

Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces

Author(s): Jaume Llibre, Yuzhou Tian
Published in: Zeitschrift fur Angewandte Mathematik und Physik, 2021, ISSN 0044-2275
Publisher: Birkhauser Verlag
DOI: 10.1007/s00033-020-01450-1

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

Author(s): Jaume Giné; Maite Grau; Jaume Llibre
Published in: Expositiones Mathematicae, Issue 7, 2022, ISSN 0723-0869
Publisher: 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

Author(s): JOHANA JIMENEZ, JAUME LLIBRE, JOAO C. MEDRADO
Published in: Electronic Journal of Differential Equations, 2020, ISSN 1072-6691
Publisher: Texas State University - San Marcos

Analysis of interactions between human immune system and a pathogenic virus

Author(s): G Moza, LV Vesa
Published in: Carpathian Journal of Mathematics, Issue 39, 2023, ISSN 1843-4401
Publisher: SINUS Association
DOI: 10.37193/cjm.2023.02.06

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

Author(s): Jaume Llibre, Víctor F. Sirvent
Published in: J. Difference Equ. Appl., 2019, ISSN 1023-6198
Publisher: Taylor & Francis
DOI: 10.1080/10236198.2019.1606216

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

Author(s): Constantinescu, Dana; Tigan, Gheorghe; Zhang, Xiang
Published in: Open Research Europe, Issue 41, 2021, ISSN 2732-5121
Publisher: European Commission
DOI: 10.12688/openreseurope.13590.1

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

Author(s): Zhifei Guo, Jaume Llibre
Published in: Qual. Theory Dyn. Syst., 2022, ISSN 1575-5460
Publisher: Springer Verlag
DOI: 10.1007/s12346-022-00643-5

The limit cycles of the Higgins-Selkov systems

Author(s): Hebai Chen, Jaume Llibre, Yilei Tang
Published in: J. Nonlinear Sci., Issue 6 issues/vol./yr., 2021, ISSN 0938-8974
Publisher: Springer Verlag
DOI: 10.1007/s00332-021-09742-0

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

Author(s): J. Llibre, C. Valls
Published in: Boletín de la Sociedad Matemática Mexicana, 2022, ISSN 2296-4495
Publisher: Birkhauser
DOI: 10.1007/s40590-022-00433-8

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

Author(s): Maoan Han, Jaume Llibre, Yun Tian
Published in: Mathematics, 2020, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math8071137

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

Author(s): J. Llibre, X. Zhang
Published in: Proceedings of the American Mathematical Society, 2021, ISSN 1088-6826
Publisher: American Mathematical Society
DOI: 10.1090/proc/15601

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

Author(s): D. Constantinescu
Published in: Issue 49, 2022, ISSN 2271-2097
Publisher: ITM Web of Conferences
DOI: 10.1051/itmconf/20224902002

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

Author(s): L. Bucur
Published in: 2022, ISSN 2271-2097
Publisher: ITM Web of Conferences
DOI: 10.1051/itmconf/20224901002

A mathematical model of infectious disease transmission

Author(s): Florea Aurelia; Lăzureanu Cristian
Published in: ITM Web of Conferences, Issue 62, 2020, ISSN 2271-2097
Publisher: EDP Sciences
DOI: 10.1051/itmconf/20203402002

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

Author(s): Munteanu Florian
Published in: ITM Web of Conferences, Vol 34, p 03010 (2020), Issue 55, 2020, ISSN 2271-2097
Publisher: EDP Sciences
DOI: 10.1051/itmconf/20203403010

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

Author(s): Danet Cristian Paul
Published in: ITM Web of Conferences, Issue 34, 2020, ISSN 2271-2097
Publisher: EDP Sciences
DOI: 10.1051/itmconf/20203403005

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

Author(s): E. Musafirov, A. Grin, A. Pranevich, F. Munteanu, C. Sterbeti
Published in: ITM Web of Conferences, 2022, ISSN 2271-2097
Publisher: edpsciences
DOI: 10.1051/itmconf/20224902006

A Spray Theory for the Geometric Method in Hydrodynamics

Author(s): Cismas, Emanuel Ciprian
Published in: Issue 33, 2019
Publisher: arxiv
DOI: 10.48550/arxiv.1909.13483

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