Publications 2021:
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M. E. Anacleto, J. Llibre, C. Valls, C. Vidal.
Limit cycles of discontinuous piecewise differential systems formed by linear centers in $R^2$ and separated by two circles.
Nonlinear Anal. Real World Appl., 60, 103281, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

I. Basak, J. Llibre.
Dynamics of two Einstein-Friedmann cosmological models.
Eur. Phys. J. Plus, 136, 8:1-7, 2021. [DOI]
 [Preprint] [Abstract]

R. Benterki, L. Damene, J. Llibre.
The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves II.
Differ. Equ. Dyn. Syst., 2021. [DOI] (Published Online)
 [Preprint] [Abstract]

R. Benterki, J. Llibre.
The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves i.
Dyn. Contin. Discrete Impuls. Syst. Ser A: Math Anal., 28, 153-192, 2021.
 [Preprint] [Abstract]

C. A. Buzzi, Y. R. Carvalho, A. Gasull.
The local period function for Hamiltonian systems with applications.
J. Differential Equations, 280, 590-617, 2021. [DOI]
 [Preprint] [Abstract]

C. A. Buzzi, Y. R. Carvalho, A. Gasull.
Limit cycles for some families of smooth and non-smooth planar systems.
Nonlinear Anal., 207, 112298:1-13, 2021. [DOI]
 [Preprint] [Abstract]

T. Chen, S. Li, J. Llibre.
Phase portraits and bifurcation diagram of the Gray-Scott model.
J. Math. Anal. Appl., 496, 124840, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Cima, A. Gasull, V. Mañosa.
Phase portraits of random planar homogeneous vector fields.
Qual. Theory Dyn. Syst., 20(3), 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Cima, A. Gasull, V. Mañosa.
Stability index of linear random dynamical systems.
Electron. J. Qual. Theo., 2021(15), 1-27, 2021. [DOI]
 [Preprint] [Abstract]

R. Colucci, E. Diz Pita, M. V. Otero Espinar.   NEW 2021-03-12
Dynamics of a two prey and one predator system with indirect effect.
Mathematics, 9, 436:1-22, 2021. [DOI]
 [Abstract] [Full PDF]

M. Corbera, C. Valls.
Reversible polynomial Hamiltonian systems of degree 3 with nilpotent saddles.
Discrete Contin. Dyn. Syst. Ser. B, 26(6), 3209-3233, 2021. [DOI]
 [Preprint] [Abstract]

K. Dias, A. Garijo.   NEW 2021-03-12
On the separatrix graph of a rational vector field on the Riemann sphere.
J. Differential Equations, 282, 541-565, 2021. [DOI]
 [Preprint] [Abstract]

E. Diz Pita, J. Llibre, M. V. Otero Espinar, C. Valls.
The zero-Hopf bifurcations in the Kolmogorov systems of degree 3 in $R^3$.
Commun. Nonlinear Sci. Numer. Simul., 95, 105621, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

D. Djedid, J. Llibre, A. Makhlouf.
Periodic orbits bifurcating from a Hopf equilibrium of 2-dimensional polynomial Kolmogorov systems of arbitrary degree.
Chaos Solitons Fractals, 142, 110489, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. Esteban, J. Llibre, C. Valls.
The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line.
Chaos, 31, 043112:1-18, 2021. [DOI]
 [Preprint] [Abstract]

E. Freire, E. Ponce, J. Torregrosa, F. Torres.
Limit cycles from a monodromic infinity in planar piecewise linear systems.
J. Math. Anal. Appl., 496, 124818, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

B. García, J. Llibre, A. Lombardero, J. S. Pérez del Río.
Analytic integrability of quasi-homogeneous systems via the Yoshida method.
J. Symbolic Comput., 104, 960-980, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

I. A. García, J. Giné, J. Llibre, S. Maza.
Vanishing set of inverse Jacobi multipliers and attractor/repulsor sets.
Chaos, 31, 013113:1-9, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Gasull.   NEW 2021-04-15
Quasi tots els camins porten a un capicua.
Semagames, 130, 17-18, 2021.
 [Preprint] [Full PDF]

J. Giné, L. F. d. S. Gouveia, J. Torregrosa.
Lower bounds for the local cyclicity for families of centers.
J. Differential Equations, 275, 309-331, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Giné, J. Llibre.
A new sufficient condition in order that the real Jacobian conjecture in $R^2$ holds.
J. Differential Equations, 281, 333-340, 2021. [DOI]
 [Preprint] [Abstract]

J. Ginoux, J. Llibre, C. Valls.
Dynamics and Darboux integrability of the $D_2$ polynomial vector fields of degree 2 in $R^3$.
Math. Phys. Anal. Geom., 24, 1:1-16, 2021. [DOI]
 [Preprint] [Abstract]

L. F. d. S. Gouveia, J. Torregrosa.
Lower bounds for the local cyclicity of centers using high order developments and parallelization.
J. Differential Equations, 271, 447-479, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

L. F. d. S. Gouveia, J. Torregrosa.
Local cyclicity in low degree planar piecewise polynomial vector fields.
Nonlinear Anal. Real World Appl., 60, 103278, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. R. A. Gouveia, J. Llibre, L. A. Roberto.
Phase portraits of the quadratic polynomial Liénard differential systems.
Proc. Roy. Soc. Edinburgh Sect. A, 151, 202-216, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. L. G. Guirao, J. Llibre, J. A. Vera, B. A. Wade.
Periodic solutions and their stability for some perturbed Hamiltonian systems.
Int. J. Geom. Methods Mod. Phys., 18(1), 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

R. Huzak, D. Rojas.
Period function of planar turning points.
Electron. J. Qual. Theo., 2021(16), 1-21, 2021. [DOI]
 [Preprint] [Abstract]

S. Kassa, J. Llibre, A. Makhlouf.   NEW 2021-03-12
Limit cycles bifurcating from a zero-Hopf equilibrium of a 3-dimensional continuous differential system.
Sao Paulo J. Math. Sci., 8 pp., 2021. [DOI]
 [Preprint] [Abstract]

T. Li, J. Llibre.
On the 16-th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems.
J. Dyn. Diff. Equat., 2021. [DOI] (Published Online)
 [Preprint] [Abstract]

T. Li, J. Llibre.
Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary.
Phys. D, 419, 132855:1-13, 2021. [DOI]
 [Preprint] [Abstract]

C. Liu, C. Li, J. Llibre.   NEW 2021-02-19
The cyclicity of the period annulus of a reversible quadratic system.
Proc. Roy. Soc. Edinburgh Sect. A, 1-10, 2021. [DOI] (Published online)
 [Preprint] [Abstract]

J. Llibre, M. Mousavi.
Phase portraits of the Higgins-Selkov system.
Discrete Contin. Dyn. Syst. Ser. B, 2021. [DOI] (Published online)
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, A. Murza.
Polynomial vector fields on the Clifford torus.
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 31(4), 2150057:1-5, 2021. [DOI]
 [Preprint] [Abstract]

J. Llibre, R. D. S. Oliveira, Y. Zhao.
On the birth and death of algebraic limit cycles in quadratic differential systems.
European J. Appl. Math., 32, 317-336, 2021. [DOI]
 [Preprint] [Abstract]

J. Llibre, A. Sá.
Minimal set of periods for continuous self-maps of the eight space.
Fixed Point Theory Algorithms Sci. Eng., 2021(3), 1-26, 2021. [DOI]
 [Preprint] [Abstract]

J. Llibre, Y. Tian.
Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces.
Z. Angew. Math. Phys., 72, 15, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, C. Valls.
The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems.
Proc. Amer. Math. Soc., 149(1), 135-141, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, C. Valls.
A sufficient condition for the real Jacobian conjecture in $R^2$.
Nonlinear Anal. Real World Appl., 60, 103298:1-10, 2021. [DOI]
 [Preprint] [Abstract]

J. Llibre, C. Valls.
Configurations of the topological indices of the planar polynomial differential systems of degree (2,m).
Results Math., 76, 21, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, C. Valls.
Rational limit cycles on Abel equations.
Commun. Pure Appl. Anal., 20(3), 2021. [DOI]
 [Preprint] [Abstract]

J. Llibre, C. Valls.
Phase portraits of uniform isochronous centers with homogeneous nonlinearities.
J. Dyn. Control Syst., 2021. [DOI] (Published Online)
 [Preprint] [Abstract]

J. Llibre, X. Zhang.
A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems.
Exposition. Math., 39, 48-61, 2021. [DOI]
 [Preprint] [Abstract]

D. Marín, J. Villadelprat.
Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting.
J. Differential Equations, 275, 684-732, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. Ollé, Ò. Rodríguez, J. Soler.   NEW 2021-01-13
Transit regions and ejection/collision orbits in the RTBP.
Commun. Nonlinear Sci. Numer. Simul., 94, 105550, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

I. Sánchez Sánchez, J. Torregrosa.
Criticality via first order development of the period constants.
Nonlinear Anal., 203, 112164:1-21, 2021. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

Q. Zaldo-Aubanell, I. Serra, J. Sardanyés, Ll. Alsedà, R. Maneja.   NEW 2020-12-22
Reviewing the reliability of Land Use and Land Cover Data in studies relating human health to the environment.
Environmental Research, 194, 110578, 2021. [DOI]
 [Abstract]