Publications 2020:
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A. Algaba, C. García, J. Giné, J. Llibre.
Orbitally universal centers.
Nonlinear Anal., 195, 111746:1-10, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.
Global topological configurations of singularities for the whole family of quadratic differential systems.
Qual. Theory Dyn. Syst., 19, 51:1-32, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.   NEW 2020-07-31
Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point.
Rend. Circ. Mat. Palermo (2), 2020. [DOI] (Published Online)
 [Abstract]

K. Baranski, N. Fagella, X. Jarque, B. Karpinska.
Fatou components and singularities of meromorphic functions.
Proc. Roy. Soc. Edinburgh Sect. A, 150, 633-654, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

L. Barreira, J. Llibre, C. Valls.
Bounded polynomial vector fields in $R^2$ and $R^n$.
J. Differential Equations, 268, 4416-4422, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

L. Barreira, J. Llibre, C. Valls.
Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis.
Electron. J. Differential Equations, 2020(57), 1-14, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

L. Barreira, J. Llibre, C. Valls.
Integrability and zero-Hopf bifurcation in the Sprott A system.
Bull. Sci. Math., 162, 102874:1-16, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. M. Benini, N. Fagella.   NEW 2020-06-15
A bound on the number of rationally invisible repelling orbits.
Adv. Math., 370, 107214:1-28, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

R. Benterki, J. Llibre.
The centers and their cyclicity for a class of polynomial differential systems of degree 7.
J. Comput. Appl. Math., 368(112456), 1-16, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

R. Benterki, J. Llibre.
Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points.
Mathematics, 8(755), 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Buica, A. Gasull.
Many periodic solutions for a second order cubic periodic differential equation.
Monatsh. Math., 2020. [DOI] (Published online)
 [Preprint]

C. A. Buzzi, J. Llibre, R. Pazim.
On the dynamics of the Euler equations on SO(4).
Dyn. Syst., 35(2), 361-368, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

C. A. Buzzi, J. Llibre, R. A. T. Santos.
Final evolutions of a class of May-Leonard Lotka-Volterra systems.
J. Nonlinear Math. Phys., 27(2), 267-278, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

C. A. Buzzi, J. C. Medrado, J. Torregrosa.
Limit cycles in 4-star-symmetric planar piecewise linear systems.
J. Differential Equations, 268(5), 2414-2434, 2020. [DOI]
 [Preprint] [Direct Shared Link] [Abstract] [Preprint at DDDUAB]

B. Campos, J. Canela, P. Vindel.
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials.
Commun. Nonlinear Sci. Numer. Simul., 82, 105026:1-19, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. R. Cândido, J. Llibre, C. Valls.
Non-existence, existence, and uniqueness of limit cycles for a generalization of the Van der Pol-Duffing and the Rayleigh-Duffing oscilators.
Phys. D, 407, 132458:1-4, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. L. Cardoso, J. Llibre, D. D. Novaes, D. J. Tonon.
Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields.
Dyn. Syst., 1-25, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

T. Chen, S. Li, J. Llibre.
Z2-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields.
J. Differential Equations, 269, 832-861, 2020. [DOI]
 [Preprint] [Abstract]

T. Chen, S. Li, J. Llibre.
Z2-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields.
J. Differential Equations, 269, 832-861, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Cima, A. Gasull, V. Mañosa.
A dynamic Parrondo's paradox for continuous seasonal systems.
Nonlinear Dynam., 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Cima, A. Gasull, F. Mañosas.
A note on the Lyapunov and Period constants.
Qual. Theory Dyn. Syst., 19, 44:1-13, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

B. Coll, A. Gasull, R. Prohens.
Asymptotic dynamics of a difference equation with a parabolic equilibrium.
Qual. Theory Dyn. Syst., 19, 2020. [DOI] (Published online)
 [Preprint] [Abstract]

M. Corbera, J. Llibre, P. Yuan.
On the convex central configurations of the symmetric (l+2)-body problem.
Regul. Chaotic Dyn., 25(3), 250-272, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. Corbera, C. Valls.
Global phase portraits of Z2-Symmetric planar polynomial Hamiltonian systems of degree three with a nilpotent saddle at the origin.
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 30(1), 2050006:1-30, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. Corbera, C. Valls.
Nilponent saddles of linear plus cubic homogeneous polynomial reversible vector fields.
Bull. Sci. Math., 162, 102873:1-18, 2020. [DOI]
 [Preprint] [Abstract]

L. P. C. Cruz, V. G. Romanovskii, J. Torregrosa.
The center and cyclicity problems for quadratic linear-like reversible systems.
Nonlinear Anal., 190, 111593: 1-19, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

L. P. C. Cruz, J. Torregrosa.
A Bendixson-Dulac theorem for some piecewise systems.
Nonlinearity, 33, 2455-2480, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Feddaoui, J. Llibre, A. Makhlouf.
4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory.
Int. J. Dyn. Syst. Differ. Equ., 10(4), 321-328, 2020.
 [Preprint] [Abstract]

A. Ferragut, J. Llibre.
On the polynomial solutions of the polynomial differential equations $yy'=a_0(x)+a_1(x)y+a_2(x)y^2+..+a_n(x)y^n$.
Indian J. Pure Appl. Math., 51, 217-232, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

F. Gao, J. Llibre.
Global dynamics of the Horava-Lifshitz cosmology with non-zero curvature and a wide range of potentials.
Eur. Phys. J. C Part. Fields, 80, 137:1-13, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. D. García Saldaña, A. Gasull, H. Giacomini.
A new approach for the study of limit cycles.
J. Differential Equations, 269, 6269-6292, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. D. García Saldaña, J. Llibre, C. Valls.
Nilpotent global centers of linear systems with cubic homogeneous nonlinearities.
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 30(1), 2050010:1-12, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Gasull, A. Geyer, F. Mañosas.
A Chebyshev criterion with applications.
J. Differential Equations, 269, 6641-6655, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Gasull, J. Giné, C. Valls.
Highest weak focus order for trigonometric Liénard equations.
Ann. Mat. Pur. Appl., 199, 1673-1684, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Gasull, V. Mañosa.
Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem.
Discrete Contin. Dyn. Syst. Ser. B, 25(2), 651-670, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Gasull, J. Torregrosa, X. Zhang.
Piecewise linear differential systems with an algebraic line of separation.
Electron. J. Differential Equations, 2020(19), 1-14, 2020.
 [Preprint] [Abstract] [Full PDF] [Preprint at DDDUAB]

J. Giné, J. Llibre.
Strongly formal weierstrass non-integrability for polynomial differential systems in $C^2$.
Electron. J. Qual. Theo., 2020(1), 1-16, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Giné, J. Llibre.   NEW 2020-04-21
Formal Weierstrass nonintegrability criterion for some classes of polynomial differential systems in $C^2$.
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 30(4), 2050064:1-7, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

L. F. d. S. Gouveia.
Limit cycles of small amplitude in polynomial and piecewise polynomial planar vector fields.
PhD thesis, Universitat Autònoma de Barcelona, Bellaterra, January, 2020.
 [Abstract]

L. F. d. S. Gouveia, J. Torregrosa.
24 crossing limit cycles in only one nest for piecewise cubic systems.
Appl. Math. Lett., 103, 106189, 2020. [DOI]
 [Preprint] [Direct Shared Link] [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, 1-15, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. L. G. Guirao, J. Llibre, W. Gao.
Topological entropy of continuous self-maps on closed surfaces.
J. Difference Equ. Appl., 26(2), 203-208, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

F. Güngör, J. Llibre, C. Pantazi.
Darboux integrability and dynamics of the Basener-Ross population model.
Rend. Circ. Mat. Palermo (2), 1-13, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

M. Han, J. Llibre, Y. Tian.
On the zero-Hopf bifurcatIon of the Lotka-Volterra systems in $R^3$.
Mathematics, 8, 1137:1-14, 2020. [DOI]
 [Preprint] [Abstract]

F. Ikhouane, V. Mañosa, G. Pujol.
Minor loops of the Dahl and LuGre models.
Appl. Math. Model., 77, 1679-1690, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. J. Jimenez Ruiz, J. Llibre, J. C. Medrado.
Crossing limit cycles for a class of piecewise linear differential centers separated by a conic.
Electron. J. Differential Equations, 41, 1-36, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. J. Jimenez Ruiz, J. Llibre, J. C. Medrado.
Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve.
Electron. J. Qual. Theo., 2020(19), 1-48, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

S. Kassa, J. Llibre, A. Makhlouf.   NEW 2020-07-27
N-dimensional zero-Hopf bifurcation of polynomial differential systems via averaging theory of second order.
J. Dyn. Control Syst., 2020. [DOI] (Published Online)
 [Preprint] [Abstract]

S. Li, J. Llibre.
Phase portraits of planar piecewise linear refracting systems: Focus-Saddle case.
Nonlinear Anal. Real World Appl., 56, 103153:1-11, 2020.
 [Preprint] [Abstract]

J. Llibre.
On the centers of cubic polynomial differential systems with four invariant straight lines.
Topol. Methods Nonlinear Anal., 55(2), 2020. (Published online)
 [Preprint] [Abstract]

J. Llibre, A. Makhlouf.
Periodic solutions for a class of non-autonomous Newton differential equations.
Differ. Equ. Dyn. Syst., 28(2), 373-379, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, A. Makhlouf.
On the periodic solutions of the relativistic driven harmonic oscillator.
J. Math. Phys., 61, 012501:1-6, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, Y. P. Martinez Mancilla.
Dynamics of a family of Lotka-Volterra systems in $R^3$.
Nonlinear Anal., 199, 111915:1-15, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, Y. P. Martinez Mancilla.
Dynamics of a competitive Lotka-Volterra systems in $R^3$.
Acta Appl. Math., 2020. [DOI] (Published Online)
 [Preprint] [Abstract]

J. Llibre, Y. P. Martinez Mancilla, C. Valls.
On the global dynamics of a three-dimensional forced-damped differential system.
J. Nonlinear Math. Phys., 27(3), 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, Y. P. Martinez Mancilla, C. Valls.   NEW 2020-05-08
Global dynamics of a Lotka-Volterra system in $R^3$.
J. Nonlinear Math. Phys., 27(3), 509-519, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, Y. P. Martinez Mancilla, C. Valls.
Limit cycles bifurcating of Kolmogorov systems in $R^2$ and in $R^3$.
Commun. Nonlinear Sci. Numer. Simul., 91, 105401:1-10, 2020. [DOI]
 [Preprint] [Abstract]

J. Llibre, L. d. A. S. Menezes.
The Markus–Yamabe conjecture does not hold for piecewise discontinuous linear differential systems separated by one straight line.
J. Dyn. Diff. Equat., 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, L. d. A. S. Menezes.
On the limit cycles of a class of discontinuous piecewise linear differential systems.
Discrete Contin. Dyn. Syst. Ser. B, 25(5), 1835-1858, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, M. Messias, A. C. Reinol.   NEW 2020-06-29
Global dynamics and bifurcation of periodic orbits in a modified Nosé-Hoover oscillator.
J. Dyn. Control Syst., 2020. [DOI]
 [Preprint] [Abstract]

J. Llibre, A. Murza, C. Valls.
On a conjecture on the integrability of Liénard systems.
Rend. Circ. Mat. Palermo (2), 69, 209-216, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, A. Nabavi, M. Mousavi.
Limit cycles bifurcating from a family of reversible quadratic centers via averaging theory.
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 30(4), 2050051:1-8, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, D. D. Novaes, C. A. B. Rodrigues.
Bifurcations from families of periodic solutions in piecewise differential systems.
Phys. D, 404, 132342:1-12, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, D. D. Novaes, I. O. Zeli.
Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems.
Rev. Mat. Iberoam., 36(1), 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, R. D. S. Oliveira, C. A. B. Rodrigues.
Limit cycles for two classes of control piecewise linear differential systems.
Sao Paulo J. Math. Sci., 1-17, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, W. F. Pereira, C. Pessoa.   NEW 2020-06-02
Phase portraits of Bernoulli quadratic polynomial differential systems.
Electron. J. Differential Equations, 2020(48), 1-19, 2020.
 [Preprint] [Abstract]

J. Llibre, W. F. Pereira, C. Pessoa.   NEW 2020-06-02
Phase portraits of Bernoulli quadratic polynomial differential systems.
Electron. J. Differential Equations, 2020(48), 1-19, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, O. Ramírez.
Gradient systems of harmonic polynomials.
J. Differential Equations, 269, 10073-10084, 2020. [DOI]
 [Preprint] [Abstract]

J. Llibre, R. O. Ramírez.
Integrability by separation of variables.
Phys. D, 409, 132523:1-22, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, R. O. Ramírez, V. Ramírez.
Integrability of a class of N-dimensional Lotka-Volterra and Kolmogorov systems.
J. Differential Equations, 269, 2503-2531, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, R. O. Ramírez, N. Sadovskaia.
Differential equations with a given set of solutions.
Appl. Math. Comput., 365, 124659:1-20, 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, V. F. Sirvent.
Periodic structure of transversal maps on sum-free products of spheres.
J. Difference Equ. Appl., 25(5), 619-629, 2020. [DOI]
 [Preprint] [Abstract]

J. Llibre, V. F. Sirvent.
Periods of holomorphic maps on compact Riemann surfaces and product of spheres.
J. Difference Equ. Appl., 2020.
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, V. F. Sirvent.
Periodic structure of transversal maps on sum-free products of spheres.
J. Difference Equ. Appl., 25(5), 619-629, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, C. Valls.
Global qualitative dynamics of the brusselator system.
Math. Comput. Simulation, 170, 107-114, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, C. Valls.
Centers of planar generalized Abel equations.
J. Differential Equations, 268, 6481-6487, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

J. Llibre, D. Xiao.
On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems.
Pacific J. Math., 306(2), 611-644, 2020. [DOI]
 [Preprint] [Abstract]

A. Nurtay, M. G. Hennessy, Ll. Alsedà, S. F. Elena, J. Sardanyés.   NEW 2020-06-29
Host-virus evolutionary dynamics with specialist and generalist infection strategies: bifurcations, bistability, and chaos.
Chaos, 30(5), 053128:1-17, 2020. [DOI]
 [Abstract]

D. Rojas.
Asymptotic development of an integral operator and boundedness of the criticality of potential centers.
J. Dyn. Diff. Equat., 32(2), 665-704, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

D. Rojas.
Resonance of bounded isochronous oscillators.
Nonlinear Anal., 192, 111680:1-10, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

D. Rojas, P. J. Torres.
Bifurcation of relative equilibria generated by a circular vortex path in a circular domain.
Discrete Contin. Dyn. Syst. Ser. B, 25(2), 749-760, 2020. [DOI]
 [Preprint] [Abstract] [Preprint at DDDUAB]

A. Vajdi, D. Juher, J. Saldaña, C. Scoglio.
A multilayer temporal network model for STD spreading accounting for permanent and casual partners.
Sci. Rep., 10, 3846:1-12, 2020.
 [Abstract] [Full PDF] [Preprint at DDDUAB]