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Resultats globals: 9 registres trobats en 0.02 segons.
Articles, 9 registres trobats
Articles 9 registres trobats  
1.
32 p, 1.1 MB Phase portraits and bifurcation diagram of the Gray-Scott model / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Li, Shimin (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We give a complete classification of the phase portraits in the Poincaré disk for the cubic polynomial systems ˙ x = 1−x−axy2, ˙ y = −by + axy2, in R2 according with the values of its two parameters a and b. [...]
2021 - 10.1016/j.jmaa.2020.124840
Journal of mathematical analysis and applications, Vol. 496, Issue 2 (April 2021) , art. 124840  
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2.
30 p, 951.8 KB On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Xiao, Dongmei (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can exhibit. Moreover, we analyze the possible configurations of these centers with respect to the invariant coordinate axes, and obtain that the real algebraic curve xy(a+bx+cy+dx2+exy+fy2)=h has at most four families of level ovals in R2 for all real parameters a,b,c,d,e,f and h.
2020 - 10.2140/pjm.2020.306.611
Pacific Journal of Mathematics, Vol. 306, Issue 2 (2020) , p. 611-644  
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3.
14 p, 336.3 KB On the centers of cubic polynomial differential systems with four invariant straight lines / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Assume that a cubic polynomial differential system in the plane has four invariant straight lines in generic position, i. e. they are not parallel and no more than two straight lines intersect in a point. [...]
2020 - 10.12775/TMNA.2020.004
Topological Methods in Nonlinear Analysis, Vol. 55, Issue 2 (June 2020) , p. 387-402  
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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
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5.
14 p, 298.1 KB Nilpotent global centers of linear systems with cubic homogeneous nonlinearities / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
In this paper, we characterize the global nilpotent centers of polynomial differential systems of the linear form plus cubic homogeneous terms.
2020 - 10.1142/S0218127420500108
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 1 (January 2020) , art. 2050010  
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6.
18 p, 299.1 KB Linear type global centers of linear systems with cubic homogeneous nonlinearities / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i. [...]
2019 - 10.1007/s12215-019-00433-0
Rendiconti del Circolo Matematico di Palermo, vol. 69 (July 2019) p. 771-785  
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7.
15 p, 383.0 KB Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields / Colak, Ilker (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
Following the work done in [8] we provide the bifurcation diagrams for the global phase portraits in the Poincaré disk of all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields.
2017 - 10.1016/j.jde.2017.02.001
Journal of differential equations, Vol. 262 (2017) , p. 5518-5533  
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8.
39 p, 577.9 KB Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields / Colak, Ilker (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We provide normal forms and the global phase portraits in the Poincaré disk for all the Hamiltonian non-degenerate centers of linear plus cubic homogeneous planar polynomial vector fields.
2014 - 10.1016/j.jde.2014.05.024
Journal of differential equations, Vol. 257 (2014) , p. 1623-1661  
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9.
34 p, 486.5 KB Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields / Colak, Ilker (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
As a natural continuation of the work done in [7] we provide the bifurcation diagrams for the global phase portraits in the Poincaré disk of all the Hamiltonian linear type centers of linear plus cubic homogeneous planar polynomial vector fields.
2015 - 10.1016/j.jde.2014.10.006
Journal of differential equations, Vol. 258 (2015) , p. 846-879  
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