Publications – Dynamical Systems: Theory, mathematical modelization and applications

Books

Ronaldo A. Garcia, Clodoaldo Grotta Ragazzo, Luis Fernando Mello, Marco Antonio Teixeira and Joan Torregrosa, Stability and Bifurcation – Dedicated to Jorge Sotomayor (in memoriam). , 2025.
Colin J. Christopher, Chengzhi Li and Joan Torregrosa, Limit Cycles of Differential Equations. Birkhäuser Cham, 2024.
Jaume Llibre, Rafael Orlando Ramírez and Valentín Ramírez, Dynamics through first-order differential equations in the configuration space. Dynamics through First-Order Differential Equations in the Configuration Space, Birkhäuser Cham, 2023.

Articles

2025

Joan Carles Artés, Laurent Cairó and Jaume Llibre. Phase portraits of the family IV of the quadratic polynomial differential systems. in Qual. Theory Dyn. Syst., 24(Article number 66). 2025. [http://dx.doi.org/10.1007/s12346-025-01227-9] [Q1, 74/332 (Mathematics, Applied), 1.900]
Anna Cima, Armengol Gasull, Víctor Mañosa and Francesc Mañosas. Invariant graphs and dynamics of a family of continuous piecewise linear planar maps. in Qual. Theory Dyn. Syst., 24(70). 103 pp., 2025. [http://dx.doi.org/10.1007/s12346-025-01221-1] [Q1, 74/332 (Mathematics, Applied), 1.900]
Armengol Gasull and Paulo Santana. A note on Hilbert 16th problem. in Proc. Amer. Math. Soc., 153(2). 669-677, 2025. [http://dx.doi.org/10.1090/proc/17116] [Q2, 193/490 (Mathematics), 0.800]
Armengol Gasull and David Rojas. Monotonous period function for equivariant differential equations with homogeneous nonlinearities. in Mediterranean J. Math., 22(112). 2025. [Q1, 100/490 (Mathematics), 1.100]
Maria Jesús Álvarez, Bartomeu Coll, Armengol Gasull and Rafel Prohens. More limit cycles for complex differential equations with three monomials. in J. Differential Equations, 416, 1071–1098, 2025. [http://dx.doi.org/10.1016/j.jde.2024.10.013] [Q1, 18/490 (Mathematics), 2.400]
Claudio A. Buzzi, Armengol Gasull and Paulo Santana. On the Cyclicity of hyperbolic polycycles. in J. Differential Equations, 429, 646-677, 2025. [http://dx.doi.org/10.1016/j.jde.2025.02.061] [Q1, 18/490 (Mathematics), 2.400]
Armengol Gasull, Luiz Fernando da Silva Gouveia and Paulo Santana. On the limit cycles of a quartic model for evolutionary stable strategies. in Nonlinear Anal. Real World Appl., 84, 104313, 2025. [http://dx.doi.org/10.1016/j.nonrwa.2024.104313] [Q1, 81/332 (Mathematics, Applied), 1.800]
Rafael Ortega and David Rojas. Relativistic effects in the dynamics of a particle in a Coulomb field. in Phys. D, 472, 134534, 2025. [Q1, 5/61 (Physics, Mathematical), 2.700]
Leonardo Pereira Costa da Cruz, Alex Carlucci Rezende and Joan Torregrosa. Coexistence of analytic and piecewise analytic limit cycles in planar piecewise quadratic differential systems. in Qual. Theory Dyn. Syst., 24(103). 2025. [http://dx.doi.org/10.1007/s12346-025-01252-8] [Q1, 74/332 (Mathematics, Applied), 1.900]
Joan Torregrosa. Cubic planar vector fields with high local cyclicity. in Sao Paulo J. Math. Sci., 19(4). 2025. [http://dx.doi.org/10.1007/s40863-024-00486-9] [Q4, 396/490 (Mathematics), 0.400]
Peter de Maesschalck and Joan Torregrosa. Limit cycles and critical periods with non-hyperbolic slow-fast systems. in J. Differential Equations, 433, 113307 (24 pages), 2025. [http://dx.doi.org/https://doi.org/10.1016/j.jde.2025.113307] [Q1, 18/490 (Mathematics), 2.400]
Jaume Giné and Joan Torregrosa. Limit cycles of homogeneous polynomial Kukles differential systems. in Math. Comput. Simulation, 237, 335-343, 2025. [http://dx.doi.org/10.1016/j.matcom.2025.04.045] [Q1, 4/332 (Mathematics, Applied), 4.400]
Leonardo Pereira Costa da Cruz, Joan Torregrosa, Miguel Berdugo and Josep Sardanyés. Resource-consumer dynamics in drylands: Modeling the role of plant-plant facilitation-competition shifts with a piecewise system. in Phys. D, 473(134548). 11 pp., 2025. [http://dx.doi.org/10.1016/j.physd.2025.134548] [Q1, 5/61 (Physics, Mathematical), 2.700]
David Marín and Jordi Villadelprat. The cyclicity of hyperbolic hemicycles. in J. Differential Equations, 433, 113281, 2025. [http://dx.doi.org/https://doi.org/10.1016/j.jde.2025.113281] [Q1, 18/490 (Mathematics), 2.400]
Bacelar, Leandro; Llibre, Jaume; Reversible nilpotent centers with cubic nonlinearities. Rend. Circ. Mat. Palermo (2) 74 (2025), no. 5, 138. https://doi.org/10.1007/s12215-025-01256-y
Bakhshalizadeh, Ali; Llibre, Jaume; Rezende, Alex C.; Global dynamics analysis of a class of quadratic polynomial differential systems with an invariant plane in R3. NoDEA Nonlinear Differential Equations Appl. 32 (2025), no. 4, Paper No. 77. https://doi.org/10.1007/s00030-025-01057-3
Llibre, Jaume; Valls, Claudia; Polynomial differential systems with invariant algebraic curves of arbitrary degree formed by Legendre polynomials. J. Pure Appl. Algebra 229 (2025), no. 8, Paper No. 108001. https://doi.org/10.1016/j.jpaa.2025.108001
Li, Shimin; Llibre, Jaume; Zhao, Yulin; On the index of an isolated equilibrium point for piecewise polynomial differential systems. J. Math. Anal. Appl. 551 (2025), no. 2, part 1, Paper https://doi.org/10.1016/j.jmaa.2025.129651
Llibre, Jaume; Valls, Claudia On the dynamics of the Craik-Okamoto and the Euler top. Phys. D 476 (2025), Paper No. 134684, 9 pp. 34C05 (34C45 70K42) https://doi.org/10.1016/j.physd.2025.134684
Llibre, Jaume; Tian, Renhao Phase portraits of cubic polynomial Kolmogorov differential systems having a rational first integral of degree three. J. Math. Phys. 66 (2025), no. 5, Paper No. 052702, 10 pp. https://doi.org/10.1063/5.0220041
Llibre, Jaume; Valls, Claudia On the distribution of the zeros of some polynomial maps (P,Q,R):R3→R3. J. Algebra Appl. 24 (2025), no. 8, Paper No. 2650145, 13 pp. https://doi.org/10.1142/S0219498826501458
Llibre, Jaume; Zhao, Yulin Final evolutions for Lotka-Volterra systems in R3 having a Darboux invariant. Electron. J. Differential Equations 2025, Paper No. 37, 16 pp. https://doi.org/10.58997/ejde.2025.37
Llibre, Jaume; Valls, Claudia Global asymptotic stability in quadratic systems. Electron. J. Differential Equations 2025, Paper No. 36, 12 pp. https://doi.org/10.58997/ejde.2025.36
Bao, Yu; Li, Shimin; Llibre, Jaume; Zhao, Yulin On the number of limit cycles in two classes of polynomial differential systems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 35 (2025), no. 6, Paper No. 2550070, 12 pp. https://doi.org/10.1142/S0218127425500701
Gouveia, Márcio R. A.; Llibre, Jaume; Roberto, Luci Any Phase portraits of a family of Hamiltonian cubic systems. Differ. Equ. Dyn. Syst. 33 (2025), no. 2, 747–755. https://doi.org/10.1007/s12591-024-00691-0
Li, Jie; Llibre, Jaume Phase portraits of a class of continuous piecewise linear differential systems. Differ. Equ. Dyn. Syst. 33 (2025), no. 2, 689–746. https://doi.org/10.1007/s12591-023-00666-7
Li, Jie; Llibre, Jaume Continuous-discontinuous piecewise differential systems with two pieces separated by a non-regular line. Discrete Contin. Dyn. Syst. Ser. B 30 (2025), no. 9, 3277–3287. doi:10.3934/dcdsb.2025022
Dong, Guangfeng; Llibre, Jaume The uniform isochronous centers with homogeneous nonlinearities of degree 5. J. Dyn. Control Syst. 31 (2025), no. 2, Paper No. 11, 13 pp. https://doi.org/10.1007/s10883-025-09734-3
Barreira, Luís; Llibre, Jaume; Valls, Claudia Flows with constant slope on the Klein bottle. Quaest. Math. 48 (2025), no. 3, 515–523. https://doi.org/10.2989/16073606.2024.2402926
Mancilla-Martínez, Y. Paulina; Llibre, Jaume; Valls, Claudia On the dynamics of the Muthuswamy-Chua systems in R3. Chaos 35 (2025), no. 4, Paper No. 043121, 8 pp. https://doi.org/10.1063/5.0255329
Llibre, Jaume; Sánchez, Angela C. T.; Tonon, Durval J. Limit cycles of discontinuous piecewise differential systems formed by two rigid systems separated by a straight line. NoDEA Nonlinear Differential Equations Appl. 32 (2025), no. 3, Paper No. 48, 21 pp. https://doi.org/10.1007/s00030-025-01050-w
Llibre, Jaume; Sun, Xianbo Small-amplitude periodic solutions in the polynomial jerk equation of arbitrary degree. Phys. D 476 (2025), Paper No. 134628, 11 pp. https://doi.org/10.1016/j.physd.2025.134628
Anacona, Gerardo H.; Llibre, Jaume; Freitas, Bruno On the limit cycles bifurcating from the periodic orbits of a Hamiltonian system. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 35 (2025), no. 4, Paper No. 2550040, 8 pp. https://doi.org/10.1142/S0218127425500403
Llibre, Jaume; de Moraes, Jaime R. Analytic study of two limit cycles bifurcating from a zero-Hopf equilibrium. Bol. Soc. Mat. Mex. (3) 31 (2025), no. 2, Paper No. 43, 7 pp. 3 https://doi.org/10.1007/s40590-025-00726-8
Llibre, Jaume; Valls, Claudia The global dynamics of a 3-dimensional differential system in R3 via a Darboux invariant. Acta Math. Sci. Ser. B (Engl. Ed.) 45 (2025), no. 2, 338–346. https://doi.org/10.1007/s10473-025-0204-9
Álvarez-Ramírez, Martha; Llibre, Jaume Global phase portrait of a rolling motion of ships equation. Qual. Theory Dyn. Syst. 24 (2025), no. 2, Paper No. 65, 12 pp. https://doi.org/10.1007/s12346-025-01228-8
Cufí-Cabré, Clara; Llibre, Jaume Correction to: Periods of Morse-Smale diffeomorphisms on Sn, Sm×Sn, CPn and HPn. J. Fixed Point Theory Appl. 27 (2025), no. 1, Paper No. 11, 2 pp. https://doi.org/10.1007/s11784-024-01158-z
Chen, Ting; Llibre, Jaume Topological classification of some SD Hamiltonian systems. Differ. Equ. Dyn. Syst. 33 (2025), no. 1, 97–121. https://doi.org/10.1007/s12591-023-00637-y
Braun, Francisco; Llibre, Jaume On the connection between global centers and global injectivity in the plane. Differ. Equ. Dyn. Syst. 33 (2025), no. 1, 71–79. https://doi.org/10.1007/s12591-023-00630-5
Castellanos, Víctor; Llibre, Jaume Zero-Hopf bifurcation in a family of tritrophic food chain model with Holling III-III functional response. Math. Methods Appl. Sci. 48 (2025), no. 3, 3434–3447. https://doi.org/10.1002/mma.10494
Llibre, Jaume; Xiong, Haichao; Zhang, Weinian Algebraic limit cycles of planar discontinuous piecewise linear differential systems with an angular switching boundary. J. Math. Anal. Appl. 546 (2025), no. 2, Paper No. 129224, 31 pp. https://doi.org/10.1016/j.jmaa.2025.129224
García, Isaac A.; Giné, Jaume; Llibre, Jaume Characterization of global centers by the monodromy at infinity. Commun. Nonlinear Sci. Numer. Simul. 142 (2025), Paper No. 108543, 6 pp. https://doi.org/10.1016/j.cnsns.2024.108543
Braga, Denis de Carvalho; Dias, Fabio Scalco; Llibre, Jaume; Mello, Luis Fernando The matching of two Markus-Yamabe piecewise smooth systems in the plane. Nonlinear Anal. Real World Appl. 82 (2025), Paper No. 104254, 6 pp. https://doi.org/10.1016/j.nonrwa.2024.104254
He, Dongping; Llibre, Jaume Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I). Math. Comput. Simulation 229 (2025), 743–757. https://doi.org/10.1016/j.matcom.2024.10.016
Castellanos, Víctor; Llibre, Jaume Persistence and zero-Hopf equilibrium in the tritrophic food chain model with Holling functional response. Nonlinear Anal. Real World Appl. 82 (2025), Paper No. 104232, 4 pp. https://doi.org/10.1016/j.nonrwa.2024.104232
Llibre, Jaume; Santana, Paulo Limit cycles and chaos in planar hybrid systems. Commun. Nonlinear Sci. Numer. Simul. 140 (2025), part 1, Paper No. 108382, 13 pp. https://doi.org/10.1016/j.cnsns.2024.108382

2024

Joan Carles Artés, Jaume Llibre, Dana Schlomiuk and Nicolae Vulpe. Abel quadratic differential systems of second kind. in Electron. J. Differential Equations, 2024(50). 1-38, 2024. [http://dx.doi.org/10.58997/ejde.2024.50] [Q2, 186/490 (Mathematics), 0.800]
Joan Carles Artés, Jaume Llibre and Nicolae Vulpe. Dynamics of the isotopic star differential system from the mathematical and physical point of views. in Appl. Math., 4(1). 70-78, 2024. [http://dx.doi.org/10.3390/appliedmath4010004]
Joan Carles Artés, Jaume Llibre, Dana Schlomiuk and Nicolae Vulpe. Global Analysis of Riccati Quadratic Differential Systems. in Internat. J. Bifur. Chaos Appl. Sci. Engrg., 34(1). 2450004, 2024. [http://dx.doi.org/10.1142/S0218127424500044] [Q2, 57/135 (Multidisciplinary Sciences), 1.900]
Joan Carles Artés, Marcos C. Mota and Alex Carlucci Rezende. Quadratic systems possessing an infinite elliptic-saddle or an infinite nilpotent saddle. in Internat. J. Bifur. Chaos Appl. Sci. Engrg., 34(11). 2430023, 2024. [http://dx.doi.org/10.1142/S0218127424300234] [Q2, 57/135 (Multidisciplinary Sciences), 1.900]
Joan Carles Artés. Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing One Finite Saddle-node and a Separatrix Connection. in Qual. Theory Dyn. Syst., 23(40). 2024. [http://dx.doi.org/10.1007/s12346-023-00882-0] [Q1, 74/332 (Mathematics, Applied), 1.900]
Miquel Barcelona, Àlex Haro and Josep Maria Mondelo. Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method. in SIAM J. Appl. Dyn. Syst., 23(1). 98-126, 2024. [http://dx.doi.org/10.1137/23M1547883] [Q2, 23/61 (Physics, Mathematical), 1.700]
Barril, Carles; Calsina, Àngel; Farkas, József Z. A stochastic population model with hierarchic size-structure J. Appl. Math. Comput. 70 (2024), no. 6, 5515–5542
Barril, Carles; Calsina, Àngel; Diekmann, Odo; Farkas, József Z. On hierarchical competition through reduction of individual growth J. Math. Biol. 88 (2024), no. 6, Paper No. 66, 34 pp.1134/S1560354723040093] [Q3, 232/332 (Mathematics, Applied), 0.800]
Lluís Alsedà, Liane Bordignon and Jorge Groisman. Topological entropy, sets of periods and transitivity for graph maps. in Ukraïn. Mat. Zh., 76(1). 31-47, 2024. [http://dx.doi.org/10.3842/umzh.v76i1.7659]
Anna Cima, Armengol Gasull, Víctor Mañosa and Francesc Mañosas. On some rational piecewise linear rotations. in J. Difference Equ. Appl., 30(10). 1577–1589, 2024. [http://dx.doi.org/10.1080/10236198.2023.2260898] [Q3, 167/332 (Mathematics, Applied), 1.100]
Josep Maria Cors and Miguel Garrido. Symmetric comet-type periodic orbits in the elliptic three-dimensional restricted (N+1)-body problem. in Phys. D, 470, 134426, 2024. [http://dx.doi.org/10.1016/j.physd.2024.134426] [Q1, 5/61 (Physics, Mathematical), 2.700]
Armengol Gasull. Fórmulas de integración de tipo Laisant. in Gac. R. Soc. Mat. Esp., 27(2). 258, 2024.
Armengol Gasull. From Abel’s differential equations to Hilbert’s 16th problem. in Sao Paulo J. Math. Sci., 18, 1342-1379, 2024. [http://dx.doi.org/10.1007/s40863-024-00471-2] [Q4, 396/490 (Mathematics), 0.400]
Armengol Gasull and Paulo Santana. On a variant of Hilbert’s 16th problem. in Nonlinearity, 37, 125012, 2024. [http://dx.doi.org/10.1088/1361-6544/ad8c1b] [Q2, 25/61 (Physics, Mathematical), 1.600]
Armengol Gasull, Gabriel Rondon and Paulo Ricardo da Silva. On the number of limit cycles for piecewise polynomial holomorphic systems. in SIAM J. Appl. Dyn. Syst., 23(3). 2593-2622, 2024. [http://dx.doi.org/10.1137/23M1620922] [Q2, 23/61 (Physics, Mathematical), 1.700]
Armengol Gasull and Antoni Guillamon. Palindroms: Noi, pararà pi? On?. in Notícies SCM, 53, 83-85, 2024.
Bernat Espigulé, David Juher and Joan Saldaña. Collinear fractals and Bandt’s conjecture. in Fractal Fract., 8(12). 725, 2024. [http://dx.doi.org/https://doi.org/10.3390/fractalfract8120725] [Q1, 16/135 (Mathematics, Interdisciplinary Applications), 3.600]
Álvaro Fernández-Mora, Àlex Haro and Josep Maria Mondelo. Flow map parameterization methods for invariant tori in quasi-periodic Hamiltonian systems. in SIAM J. Appl. Dyn. Syst., 23(1). 127-166, 2024. [http://dx.doi.org/10.1137/23M1561257] [Q2, 23/61 (Physics, Mathematical), 1.700]
Claudio A. Buzzi, Ana Livia Rodero and Joan Torregrosa. 3-dimensional piecewise linear and quadratic vector fields with invariant spheres. in Electron. J. Qual. Theory Differ. Equ., 43, 1-27, 2024. [http://dx.doi.org/10.14232/ejqtde.2024.1.43] [Q1, 104/490 (Mathematics), 1.100]
Peter de Maesschalck and Joan Torregrosa. Critical periods in planar polynomial centers near a maximum number of cusps. in J. Differential Equations, 380(1). 181-197, 2024. [http://dx.doi.org/10.1016/j.jde.2023.10.034] [Q1, 18/490 (Mathematics), 2.400]
Francisco Braun, Leonardo Pereira Costa da Cruz and Joan Torregrosa. On the number of limit cycles in piecewise planar quadratic differential systems. in Nonlinear Anal. Real World Appl., 79, 104124, 2024. [http://dx.doi.org/10.1016/j.nonrwa.2024.104124] [Q1, 81/332 (Mathematics, Applied), 1.800]
Alex Carlucci Rezende, Mirianne A. S. Santos and Joan Torregrosa. Period function for a family of piecewise planar Hamiltonian systems. in Internat. J. Bifur. Chaos Appl. Sci. Engrg., 34(16). 2450199 (12 pp.), 2024. [http://dx.doi.org/10.1142/S0218127424501992] [Q2, 57/135 (Multidisciplinary Sciences), 1.900]
Jaume Giné, Valery G. Romanovskii and Joan Torregrosa. Time-reversibility and integrability of p : -q resonant vector fields. in AIMS Mathematics, 9(1). 73–-88, 2024. [http://dx.doi.org/10.3934/math.2024005] [Q1, 76/332 (Mathematics, Applied), 1.800]
David Marín and Jordi Villadelprat. Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: coefficient properties. in J. Differential Equations, 404, 43-107, 2024. [http://dx.doi.org/10.1016/j.jde.2024.05.037] [Q1, 18/490 (Mathematics), 2.400]
Jorge Vicente-Puig; Ismael Hernández-Romero; Raúl Moreno; Clara Herrero; Maria S. Guillem; Andreu M. Climent; Judit Chamorro-Servent. Performance of iterative methods of ECGI in the atria. 51st International Computing in Cardiology 2024. Karlsruhe, Alemanya.
Jorge Vicente-Puig; Ismael Hernández-Romero; Ernesto Zacur; Andreu M. Climent; Maria S. Guillem; Judit Chamorro-Servent. Títol: A linear data completion problem in inverse electrocardiography. 11th International Conference “Inverse Problems: Modeling and Simulation”. Tipus de contribució: Oral. Lloc i data: Malta, juny 2024.
Baymout, Louiza; Benterki, Rebiha; Llibre, Jaume The limit cycles of a class of discontinuous piecewise differential systems. Int. J. Dyn. Syst. Differ. Equ. 13 (2024), no. 4, 339–368.
Dong, Guangfeng; Llibre, Jaume Periodic orbits for an autonomous version of the Duffing-Holmes oscillator. Nonlinear Anal. Model. Control 29 (2024), no. 6, 1120–1126.
Baymout, Louiza; Benterki, Rebiha; Llibre, Jaume Three-dimensional limit cycles generated from discontinuous piecewise differential systems separated by two intersecting planes. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 34 (2024), no. 16, Paper No. 2450204, 19 pp. https://doi.org/10.1142/S0218127424502043
Hussein, Sarbast; Llibre, Jaume On the integrability of the Sprott cubic conservative jerk system. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 34 (2024), no. 16, Paper No. 2450200, 11 pp. https://doi.org/10.1142/S0218127424502006
Braun, Francisco; Llibre, Jaume Parallel vector fields and global injectivity in two dimensions. Pacific J. Math. 333 (2024), no. 1, 1–15. https://doi.org/10.2140/pjm.2024.333.1
Llibre, Jaume; Serantola, Leonardo P. New families of global cubic centers. São Paulo J. Math. Sci. 18 (2024), no. 2, 1454–1469. https://doi.org/10.1007/s40863-024-00411-0
Llibre, Jaume On my eight articles with the Professor Jorge Sotomayor. São Paulo J. Math. Sci. 18 (2024), no. 2, 1447–1451. https://doi.org/10.1007/s40863-024-00434-7
Llibre, Jaume; Valls, Claudia Phase portraits of the equation x¨+axx˙+bx3=0. Regul. Chaotic Dyn. 29 (2024), no. 6, 825–837. https://doi.org/10.1134/S1560354724560053
Anacleto, Maria Elisa; Llibre, Jaume; Valls, Claudia; Vidal, Claudio On the crossing limit cycles created by a discontinuous piecewise differential system formed by three linear Hamiltonian saddles. Dyn. Syst. 39 (2024), no. 4, 799–822. https://doi.org/10.1080/14689367.2024.2391417
Bouaziz, Chamseddine; Llibre, Jaume; Djedid, Djamila; Makhlouf, Amar Periodic orbits in the zero-Hopf bifurcations of 3-dimensional Kolmogorov systems of degree 3. Appl. Math. E-Notes 24 (2024), 237–273.
Llibre, Jaume; Tian, Renhao Periodic orbits and non-existence of C1 first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in R4. Rend. Circ. Mat. Palermo (2) 73 (2024), no. 7, 2723–2733. https://doi.org/10.1007/s12215-024-01074-8
Li, Shimin; Llibre, Jaume; Tong, Qian Poincaré compactification for n-dimensional piecewise polynomial vector fields: theory and applications. Topology Appl. 358 (2024), Paper No. 109126, 17 pp. https://doi.org/10.1016/j.topol.2024.109126
Barreira, Luis; Llibre, Jaume; Valls, Clàudia On the global nilpotent centers of cubic polynomial Hamiltonian systems. Differ. Equ. Dyn. Syst. 32 (2024), no. 4, 1001–1011. https://doi.org/10.1007/s12591-022-00606-x
He, Dongping; Llibre, Jaume Correction to: Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (II). Mediterr. J. Math. 21 (2024), no. 7, Paper No. 192, 1 p. https://doi.org/10.1007/s00009-024-02730-0
Llibre, Jaume; Salhi, Tayeb Periodic orbits of continuous-discontinuous piecewise differential systems with four pieces separated by the curve xy=0 and formed by linear Hamiltonian systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 31 (2024), no. 4, 279–286.
Llibre, Jaume Periods of self-maps on S2 via their homology. Reprint of Ukraïn. Mat. Zh. 76 (2024), no. 1, 72–74. Ukrainian Math. J. 76 (2024), no. 1, 76–79. https://doi.org/10.1007/s11253-024-02308-9
Dong, Guangfeng; Llibre, Jaume The uniform isochronous centers with homogeneous nonlinearities of degree 6. J. Dyn. Control Syst. 30 (2024), no. 3, Paper No. 34, 23 pp. https://doi.org/10.1007/s10883-024-09703-2
Appis, Raul Felipe; Llibre, Jaume Global centers of a family of cubic systems. Aequationes Math. 98 (2024), no. 5, 1373–1389. https://doi.org/10.1007/s00010-024-01051-7
Llibre, Jaume; Valls, Claudia The classical and improved Euler-Jacobi formula and polynomial vector fields in Rn. J. Dynam. Differential Equations 36 (2024), no. 3, 2093–2110. https://doi.org/10.1007/s10884-022-10191-w
He, Dongping; Llibre, Jaume Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (II). Mediterr. J. Math. 21 (2024), no. 6, Paper No. 174, 31 pp. https://doi.org/10.1007/s00009-024-02714-0
Lima, Maurıicio F. S.; Llibre, Jaume Hopf bifurcation for a class of predator-prey system with small immigration. Electron. Res. Arch. 32 (2024), no. 7, 4604–4613. https://doi.org/10.3934/era.2024209
Llibre, Jaume; Rondón, Gabriel Global centers of a class of cubic polynomial differential systems. Rend. Circ. Mat. Palermo (2) 73 (2024), no. 5, 2141–2160. https://doi.org/10.1007/s12215-024-01034-2
Liu, Chang Jian; Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín Solution of the center problem for a class of polynomial differential systems. Acta Math. Sin. (Engl. Ser.) 40 (2024), no. 7, 1685–1696. https://doi.org/10.1007/s10114-024-0578-y
Ginoux, Jean-Marc; Meucci, Riccardo; Llibre, Jaume; Sprott, Julien Clinton; The jerk dynamics of Lorenz model. Advances in nonlinear dynamics. Vol. III, 121–129, NODYCON Conf. Proc. Ser., Springer, Cham, [2024] https://doi.org/10.1007/s10114-024-0578-y
Duran Baldissera, Maíra; Llibre, Jaume; Oliveira, Regilene Dynamics of a generalized Rayleigh system. Differ. Equ. Dyn. Syst. 32 (2024), no. 3, 933–941. https://doi.org/10.1007/s12591-022-00604-z
Bakhshalizadeh, Ali; Llibre, Jaume Phase portraits of a class of cubic systems with an ellipse and a straight line as invariant algebraic curves. Differ. Equ. Dyn. Syst. 32 (2024), no. 3, 871–907. https://doi.org/10.1007/s12591-022-00597-9
Llibre, Jaume; Salhi, Tayeb Planar quadratic differential systems with invariants of the form ax2+bxy+cy2+dx+ey+c1t. Bull. Iranian Math. Soc. 50 (2024), no. 4, Paper No. 49, 16 pp. https://doi.org/10.1007/s41980-024-00888-
Casimiro, Joyce A.; Llibre, Jaume; Limit cycles of discontinuous piecewise differential Hamiltonian systems separated by a circle, or a parabola, or a hyperbola. Math. Comput. Simulation 225 (2024), 303–312. https://doi.org/10.1016/j.matcom.2024.05.021
Giné, Jaume; Llibre, Jaume Characterization of the Riccati and Abel polynomial differential systems having invariant algebraic curves. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 34 (2024), no. 5, Paper No. 2450066, 7 pp. https://doi.org/10.1142/S0218127424500664
Baymout, Louiza; Benterki, Rebiha; Llibre, Jaume Limit cycles of the discontinuous piecewise differential systems separated by a nonregular line and formed by a linear center and a quadratic one. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 34 (2024), no. 5, Paper No. 2450058, 42 pp. https://doi.org/10.1142/S0218127424500585
Llibre, Jaume; Valls, Claudia Darboux theory of integrability in Tn. Eur. J. Math. 10 (2024), no. 2, Paper No. 26, 17 pp. https://doi.org/10.1007/s40879-024-00737-1
Llibre, Jaume; Valls, Claudia Twin quadratic polynomial vector fields in the space C3. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 31 (2024), no. 2, 121–132.
Llibre, Jaume; Valls, Claudia Global dynamics of a system coming from the study of a static star. Differ. Equ. Dyn. Syst. 32 (2024), no. 2, 607–617. https://doi.org/10.1007/s12591-021-00588-2
Llibre, Jaume; Salhi, Tayeb Phase portraits of an SIR epidemic model. Appl. Anal. 103 (2024), no. 6, 1165–1175. https://doi.org/10.1080/00036811.2023.2235390
Llibre, Jaume; Valls, Claudia Darboux theory of integrability on the Clifford n-dimensional torus. Bull. Sci. Math. 192 (2024), Paper No. 103403, 9 pp. https://doi.org/10.1016/j.bulsci.2024.103403
Llibre, Jaume; Pantazi, Chara Qualitative study of the Selkov model. J. Differential Equations 393 (2024), 155–173. https://doi.org/10.1016/j.jde.2024.02.011
Llibre, Jaume; Valls, Claudia The phase portrait of all polynomial Liénard isochronous centers. Chaos Solitons Fractals 180 (2024), Paper No. 114500, 4 pp. https://doi.org/10.1016/j.chaos.2024.114500

2023

Lluís Alsedà, Michal Misiurewicz and Rodrigo A. Pérez. Flexibility of entropies for piecewise expanding unimodal maps. 48-66, 2023. [http://dx.doi.org/10.1017/9781009278898.003]
Lluís Alsedà, David Juher, Jérôme Los and Francesc Mañosas. On families of Bowen-Series-like maps for surface groups. in Regul. Chaotic Dyn., 28(4-5). 659-667, 2023. [http://dx.doi.org/10
Calsina, Àngel; Cuadrado, Sílvia; Vidiella, Blai; Sardanyés, Josep About ghost transients in spatial continuous media Chaos Solitons Fractals 166 (2023), Paper No. 112915, 13 pp.
Barril, Carles; Bliman, Pierre-Alexandre; Cuadrado, Sílvia Final size for epidemic models with asymptomatic transmission Bull. Math. Biol. 85 (2023), no. 6, Paper No. 52, 28 pp.
Daniel Oro, Lluís Alsedà, Alan Hastings, Meritxell Genovart and Josep Sardanyés. Social copying drives a tipping point for non-linear population collapse. in Proceedings of the National Academy of Sciences, 120(11). e2214055120, 2023. [http://dx.doi.org/10.1073/pnas.2214055120]
Armengol Gasull, Antoni Guillamon and Víctor Mañosa. Counting configurations of limit cycles and centers. in Bul. Acad. Ştiinţe Repub. Mold. Mat., 101, 78-96, 2023. [http://dx.doi.org/10.56415/basm.y2023.i1.p78]
Armengol Gasull and Yulin Zhao. Existence of at most two limit cycles for some non-autonomous differential equations. in Commun. Pure Appl. Anal., 22(3). 970-982, 2023. [http://dx.doi.org/10.3934/cpaa.2023016] [Q1, 121/490 (Mathematics), 1.000]
Armengol Gasull. Linealización en sistemas dinámicos holomorfos. in Gac. R. Soc. Mat. Esp., 26(3). 518, 2023.
Antoni Ferragut, Armengol Gasull and Xiang Zhang. Meromorphic first integrals of analytic diffeomorphisms. in J. Math. Anal. Appl., 519, 126796, 2023. [http://dx.doi.org/10.1016/j.jmaa.2022.126796] [Q1, 82/490 (Mathematics), 1.200]
Armengol Gasull. Mètodes de demostració. in Mat. Mat., 3, 85, 2023.
Armengol Gasull and Hector Giacomini. Number of limit cycles for planar systems with invariant algebraic curves. in Qual. Theory Dyn. Syst., 22(2). 44:1-28, 2023. [http://dx.doi.org/10.1007/s12346-023-00746-7] [Q1, 74/332 (Mathematics, Applied), 1.900]
Bartomeu Coll, Armengol Gasull and Rafel Prohens. Probability of existence of limit cycles for a family of planar systems. in J. Differential Equations, 373, 152-175, 2023. [http://dx.doi.org/10.1016/j.jde.2023.07.015] [Q1, 18/490 (Mathematics), 2.400]
Armengol Gasull. Proof without words: tangent of pi/8. in Coll. Math. J., 54, 2023. [http://dx.doi.org/10.1080/07468342.2023.2238581]
Armengol Gasull, Florian Luca and Juan Luis Varona. Three essays on Machin’s type formulas. in Indag. Math. (N.S.), 34, 1373–1396, 2023. [http://dx.doi.org/10.1016/j.indag.2023.07.002] [Q3, 363/490 (Mathematics), 0.500]
Maria Jesús Álvarez, Armengol Gasull and Rafel Prohens. Uniqueness of limit cycles for complex differential equations with two monomials. in J. Math. Anal. Appl., 518, 126663, 2023. [http://dx.doi.org/10.1016/j.jmaa.2022.126663] [Q1, 82/490 (Mathematics), 1.200]
David Juher, David Rojas and Joan Saldaña. Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness. in Phys. D, 448, 133714, 2023. [http://dx.doi.org/10.1016/j.physd.2023.133714] [Q1, 5/61 (Physics, Mathematical), 2.700]
Jéfferson L. R. Bastos, Claudio A. Buzzi and Joan Torregrosa. Cyclicity near infinity in piecewise linear vector fields having a nonregular switching line. in Qual. Theory Dyn. Syst., 22(125). 2023. [http://dx.doi.org/10.1007/s12346-023-00817-9] [Q1, 74/332 (Mathematics, Applied), 1.900]
Alex Arenas, Antoni Garijo, Sergio Gómez Jiménez and Jordi Villadelprat. A bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading. in Chaos Solitons Fractals, 166, 112921, 2023. [http://dx.doi.org/10.1016/j.chaos.2022.112921] [Q1, 17/110 (Physics Multidisciplicar), 5.300]
David Marín, Mariana Saavedra and Jordi Villadelprat. Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centers. in Proc. Roy. Soc. Edinburgh Sect. A, 153(1). 104 – 114, 2023. [http://dx.doi.org/10.1017/prm.2021.72] [Q1, 71/490 (Mathematics), 1.300]
Alex Arenas, Antoni Garijo, Sergio Gómez Jiménez and Jordi Villadelprat. On the number of stable solutions in the Kuramoto model. in Chaos, 33, 093127, 2023. [http://dx.doi.org/10.1063/5.0161977] [Q1, 6/61 (Physics, Mathematical), 2.700]
Diz-Pita, Érika; Llibre, Jaume; Otero-Espinar, M. Victoria Study of the nonelementary singular points and the dynamics near the infinity in predator-prey systems. Computational and mathematical models in biology, 103–128, Nonlinear Syst. Complex., 38, Springer, Cham, [2023] https://doi.org/10.1007/978-3-031-42689-6_5
Llibre, Jaume; Valls, Claudia The extended 16th Hilbert problem for discontinuous piecewise systems formed by linear centers and linear Hamiltonian saddles separated by a nonregular line. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 16, Paper No. 2350196, 10 pp. https://doi.org/10.1142/S0218127423501961
Llibre, Jaume; Valls, Claudia A weakened Markus-Yamabe condition for planar polynomial differential systems of degree (1,n). Proc. Edinb. Math. Soc. (2) 66 (2023), no. 4, 1110–1118. doi:10.1017/S0013091523000615
Esteban, M.; Llibre, J.; Valls, C. An extension of the 16th Hilbert problem for continuous piecewise linear-quadratic centers separated by a non-regular line. Chaos 33 (2023), no. 12, Paper No. 123120, 9 pp. https://doi.org/10.1063/5.0167089
Jimenez, Johana; Llibre, Jaume Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder. São Paulo J. Math. Sci. 17 (2023), no. 2, 679–691. https://doi.org/10.1007/s40863-023-00377-5
Braga, Denis de Carvalho; Dias, Fabio Scalco; Llibre, Jaume; Mello, Luis Fernando 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. São Paulo J. Math. Sci. 17 (2023), no. 2, 671–678. https://doi.org/10.1007/s40863-023-00368-6
Llibre, J.; Pantazi, C. Integrability and dynamics of a simplified class B laser system. Chaos 33 (2023), no. 10, Paper No. 103119, 9 pp. https://doi.org/10.1063/5.016934
Li, Shimin; Liu, Changjian; Llibre, Jaume On the Poincaré-Bendixson formula for planar piecewise smooth vector fields. J. Nonlinear Sci. 33 (2023), no. 6, Paper No. 118, 29 pp. https://doi.org/10.1007/s00332-023-09979-x
Llibre, Jaume; Mancilla-Martínez, Y. Paulina Global attractor in the positive quadrant of the Lotka-Volterra system in R2. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 12, Paper No. 2350147, 12 pp. https://doi.org/10.1142/S021812742350147X
Llibre, Jaume; Valls, Claudia The 16th Hilbert problem for discontinuous piecewise linear differential systems separated by the algebraic curve y=xn. Math. Phys. Anal. Geom. 26 (2023), no. 4, Paper No. 25, 9 pp. https://doi.org/10.1007/s11040-023-09467-4
Llibre, Jaume; Valls, Claudia Polynomial differential systems with hyperbolic limit cycles. J. Geom. Phys. 194 (2023), Paper No. 104983, 4 pp. https://doi.org/10.1016/j.geomphys.2023.104983
Llibre, Jaume; Valls, Claudia Phase portraits on the unit sphere of the stretch-twist-fold flow. Nonlinear Anal. Model. Control 28 (2023), no. 5, 1020–1036. https://doi.org/10.15388/namc.2023.28.33088
Llibre, Jaume Some families of quadratic systems with at most one limit cycle. Bul. Acad. Ştiinţe Repub. Mold. Mat. 2023, no. 1(101), 8–15. https://doi.org/10.56415/basm.y2023.i1.p8
Giné, Jaume; Llibre, Jaume Criteria for the nonexistence of periodic orbits in planar differential systems. Bul. Acad. Ştiinţe Repub. Mold. Mat. 2023, no. 1(101), 3–7.https://doi.org/10.56415/basm.y2023.i1.p3
Llibre, Jaume; Teixeira, Marco Antonio On the periodic orbits of the continuous-discontinuous piecewise differential systems with three pieces separated by two parallel straight lines. Commun. Nonlinear Sci. Numer. Simul. 125 (2023), Paper No. 107421, 9 pp. https://doi.org/10.1016/j.cnsns.2023.107421
Llibre, Jaume On the C1 non-integrability of the autonomous differential systems. Nonlinear Anal. Real World Appl. 74 (2023), Paper No. 103943, 9 pp. https://doi.org/10.1016/j.nonrwa.2023.103943
Llibre, Jaume; Valls, Claudia Invariants of polynomial vector fields. J. Differential Equations 365 (2023), 895–904. https://doi.org/10.1016/j.jde.2023.05.024
Chen, Ting; Huang, Lihong; Llibre, Jaume Nonexistence and uniqueness of limit cycles in a class of three-dimensional piecewise linear differential systems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 6, Paper No. 2350075, 13 pp. https://doi.org/10.1142/S021812742350075X
Ripoll, J. Font. Numerical approach to an age-structured Lotka-Volterra model.
Math. Biosci. Eng., 2023, 20(9): 15603-15622. doi: 10.3934/mbe.2023696
J. Ripoll, J. Font: A Discrete Model for the Evolution of Infection Prior to Symptom Onset. Mathematics 2023, 11, 1092. https://doi.org/10.3390/math11051092
Yang, Saldaña, Scoglio. Generalized epidemic model incorporating non-Markovian infection processes and waning immunity. Physical Revier E 2023 10.1103/PhysRevE.108.014405

2022

Jordi Canela, Lluís Alsedà, Nuria Fagella and Josep Sardanyés. Dynamical mechanism behind ghosts unveiled in a map complexification. in Chaos Solitons Fractals, 156, 111780, 2022. [http://dx.doi.org/10.1016/j.chaos.2021.111780] [Q1, 1/56 (Physics, Mathematical), 7.800]
Lluís Alsedà, David Juher and Francesc Mañosas. Forward triplets and topological entropy on trees. in Discrete Contin. Dyn. Syst., 42(2). 623-641, 2022. [http://dx.doi.org/10.3934/dcds.2021131] [Q2, 105/331 (Mathematics), 1.100]
Anna Cima, Armengol Gasull and Víctor Mañosa. Asymptotic stability for block triangular maps. in Sarajevo J. Math., 18(1). 25-44, 2022. [http://dx.doi.org/10.5644/SJM.18.01.03]
Anna Cima, Armengol Gasull, Víctor Mañosa and Francesc Mañosas. Pointwise periodic maps with quantized first integrals. in Commun. Nonlinear Sci. Numer. Simul., 108, 106150:1-26, 2022. [http://dx.doi.org/10.1016/j.cnsns.2021.106150] [Q1, 5/56 (Physics, Mathematical), 3.900]
Armengol Gasull. 55 proves sense paraules. in Mat. Mat., 2022, 2:1-61, 2022.
Armengol Gasull and Clàudia Valls. Discrete Melnikov functions. in J. Difference Equ. Appl., 20(10). 1348-1361, 2022. [http://dx.doi.org/10.1080/10236198.2021.1970147] [Q3, 179/268 (Mathematics, Applied), 1.100]
Armengol Gasull. Los Babilonios y Newton. in Gac. R. Soc. Mat. Esp., 25(3). 488, 2022.
Martha Álvarez-Ramírez, Armengol Gasull and Jaume Llibre. On the equilateral pentagonal central configurations. in Commun. Nonlinear Sci. Numer. Simul., 112, 106511:1-12, 2022. [http://dx.doi.org/10.1016/j.cnsns.2022.106511] [Q1, 5/56 (Physics, Mathematical), 3.900]
Armengol Gasull, Luís Hernández-Corbato and Francisco R. Ruiz del Portal. Parrondo’s paradox for homeomorphisms. in Proc. Roy. Soc. Edinburgh Sect. A, 152, 817-825, 2022. [http://dx.doi.org/10.1017/prm.2021.28] [Q2, 89/331 (Mathematics), 1.300]
Bartomeu Coll, Armengol Gasull and Rafel Prohens. Probability of occurrence of some planar random quasi-homogeneous vector fields. in Mediterranean J. Math., 19, Article number 278, 2022. [http://dx.doi.org/10.1007/s00009-022-02198-w] [Q2, 102/331 (Mathematics), 1.100]
Armengol Gasull, Jorge Groisman and Francesc Mañosas. Regularization of Brouwer Translation Theorem. in Qual. Theory Dyn. Syst., 21, 135, 2022. [http://dx.doi.org/10.1007/s12346-022-00666-y] [Q1, 81/331 (Mathematics), 1.400]
Renato Huzak and David Rojas. Abelian integrals and non-generic turning points. in Qual. Theory Dyn. Syst., 21(77). 1-18, 2022. [http://dx.doi.org/10.1007/s12346-022-00609-7] [Q1, 81/331 (Mathematics), 1.400]
David Rojas. Oscil·ladors en ressonància. in Butl. Soc. Catalana Mat., 37(2). 137-172, 2022. [http://dx.doi.org/10.2436/20.2002.01.105]
David Rojas and Pedro J. Torres. Periodic bouncing solutions of the Lazer-Solimini equation with weak repulsive singularity. in Nonlinear Anal. Real World Appl., 64, 103441:1-13, 2022. [http://dx.doi.org/10.1016/j.nonrwa.2021.103441] [Q2, 69/268 (Mathematics, Applied), 2.000]
Leonardo Pereira Costa da Cruz and Joan Torregrosa. Bifurcation of limit cycles in piecewise quadratic differential systems with an invariant straight line. in J. Math. Anal. Appl., 514, 126256, 2022. [http://dx.doi.org/10.1016/j.jmaa.2022.126256] [Q2, 88/331 (Mathematics), 1.300]
Jackson Itikawa, Regilene D. S. Oliveira and Joan Torregrosa. First-order perturbation for multi-parameter center families. in J. Differential Equations, 309, 291-310, 2022. [http://dx.doi.org/10.1016/j.jde.2021.11.035] [Q1, 24/331 (Mathematics), 2.400]
Iván Sánchez Sánchez and Joan Torregrosa. Hopf bifurcation in 3-dimensional polynomial vector fields. in Commun. Nonlinear Sci. Numer. Simul., 105, 106068:1-13, 2022. [http://dx.doi.org/10.1016/j.cnsns.2021.106068] [Q1, 5/56 (Physics, Mathematical), 3.900]
Regilene D. S. Oliveira, Iván Sánchez Sánchez and Joan Torregrosa. Simultaneous bifurcation of limit cycles and critical periods. in Qual. Theory Dyn. Syst., 21(20). 1-35, 2022. [http://dx.doi.org/10.1007/s12346-021-00546-x] [Q1, 81/331 (Mathematics), 1.400]
Luiz Fernando da Silva Gouveia and Joan Torregrosa. The local cyclicity problem. Melnikov method using Lyapunov constants. in Proc. Edinb. Math. Soc. (2), 65, 356-375, 2022. [http://dx.doi.org/10.1017/S0013091522000128] [Q3, 222/331 (Mathematics), 0.700]
David Marín and Jordi Villadelprat. On the cyclicity of Kolmogorov polycycles. in Electron. J. Qual. Theory Differ. Equ., 2022(35). 1-31, 2022. [http://dx.doi.org/10.14232/ejqtde.2022.1.35] [Q2, 113/331 (Mathematics), 1.100]
David Marín and Jordi Villadelprat. The criticality of reversible quadratic centers at the outer boundary of its period annulus. in J. Differential Equations, 332, 123-201, 2022. [http://dx.doi.org/10.1016/j.jde.2022.05.026] [Q1, 24/331 (Mathematics), 2.400]