UAB Digital Repository of Documents 115 records found  1 - 10nextend  jump to record: Search took 0.02 seconds. 
1.
4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory / Feddaoui, Amina (University of Annaba. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics (Algeria))
The averaging theory of second order shows that for polynomial differential systems in ℝ4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.
2020 - 10.1504/IJDSDE.2020.109106
International Journal of Dynamical Systems and Differential Equations, Vol. 10, Issue 4 (2020) , p. 321-328  
2.
Gradient systems of harmonic polynomials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Oscar (Universidade Federal de Viçosa. Departamento de Matemática (Brazil))
We characterize all local phase-portraits of the finite and infinite singular points of the gradient systems defined by the real harmonic polynomials in two variables. We classify all the non-equivalent topological phase portraits of the gradient systems in the Poincaré disc defined by harmonic polynomials of degree less than five.
2020 - 10.1016/j.jde.2020.06.056
Journal of differential equations, Vol. 269, Issue 11 (November 2020) , p. 10073-10084  
3.
34 p, 1.2 MB Crossing limit cycles for a class of piecewise linear differential centers separated by a conic / Jimenez Ruiz, Jeidy Johana (Universidade Federal do Oeste da Bahia (Brasil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brasil))
These last years the study of the version of Hilbert's 16th problem for piecewise linear differential systems in the plane, has increased strongly and there are many papers studying the maximum number of crossing limit cycles when the differential system is defined in two zones separated by a straight line, in particular in [11, 13] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles, but in the papers [14, 15] it was shown that the maximum number of crossing limit cycles of piecewise linear differential centers, can change depending of the shape of the discontinuity curve. [...]
2020
Electronic journal of differential equations, Vol. 2020, Issue 41 (2020) , p. 1-36
2 documents
4.
16 p, 279.8 KB Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis / Barreira, Luis (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
A polynomial differential system of degree 2 has no global centers (that is, centers defined in all the plane except the fixed point). In this paper we characterize the global centers of cubic Hamiltonian systems symmetric with respect to the x-axis, and such that the center has purely imaginary eigenvalues.
2020
Electronic journal of differential equations, Vol. 2020 Núm. 57 (2020) , p. 1-14
2 documents
5.
20 p, 1.0 MB Phase portraits of Bernoulli quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pereira, Weber F. (Universidade Estadual Paulista. Departamento de Matemática (Brasil)) ; Pessoa, Claudio (Universidade Estadual Paulista. Departamento de Matemática (Brasil))
In this paper we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincaré disk of Bernoulli quadratic polynomial differential systems in R2.
2020
Electronic journal of differential equations, Vol. 2020, Issue 48 (2020) , p. 1-19
2 documents
6.
Z₂-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Li, Shimin (Guangdong University of Finance and Economics. School of Mathematics and Statistics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the global dynamical behavior of Z₂-equivariant cubic Hamiltonian vector fields with a linear type bi-center at (±1,0). By using a series of symbolic computation tools, we obtain all possible phase portraits of these Z₂-equivariant Hamiltonian systems.
2020 - 10.1016/j.jde.2019.12.020
Journal of differential equations, Vol. 269, Issue 1 (June 2020) , p. 832-861  
7.
A Chebyshev criterion with applications / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Geyer, Anna (Delft University of Technology. Delft Institute of Applied Mathematics (The Netherlands)) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs to determine bounds on the number of isolated periodic solutions, as well as to persistence problems of periodic solutions for perturbed Hamiltonian systems.
2020 - 10.1016/j.jde.2020.05.015
Journal of differential equations, Vol. 269, Issue 9 (October 2020) , p. 6641-6655  
8.
A new approach for the study of limit cycles / García Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Centre National de la Recherche Scientifique. Institut Denis Poisson. Université de Tours (France))
We prove that star-like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non-autonomous polynomial system or as heteroclinic solutions of a 3-dimensional polynomial system. [...]
2020 - 10.1016/j.jde.2020.04.038
Journal of differential equations, Vol. 269, Issue 7 (September 2020) , p. 6269-6292  
9.
46 p, 2.6 MB Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve / Jimenez, Jeidy J. (Universidade Federal do Oeste da Bahia (Brasil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brasil))
As for the general planar differential systems one of the main problems for the piecewise linear differential systems is to determine the existence and the maximum number of crossing limits cycles that these systems can exhibit. [...]
2020 - 10.14232/ejqtde.2020.1.19
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2020, Issue 19 (2020) , p. 1-48
2 documents
10.
Integrability of a class of N-dimensional Lotka-Volterra and Kolmogorov systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat Autònoma de Barcelona)
We study the integrability of an N-dimensional differential Kolmogorov systems of the form ̇xj=xj(aj+N∑k=1ajkxk)+xjΨ(x1,. . . ,xN), j= 1,. . . ,N, where aj, and ajk are constants for j,k = 1,. . . [...]
2020 - 10.1016/j.jde.2020.02.001
Journal of differential equations, Vol. 269, Issue 3 (July 2020) , p. 2503-2531  

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