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12 p, 630.6 KB |
On the period function in a class of generalized Lotka-Volterra systems
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Villadelprat, Jordi (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
In this note, motivated by the recent results of Wang et al. [Wang et al. , Local bifurcations of critical periods in a generalized 2D LV system, Appl. Math. Comput. 214 (2009) 17-25], we study the behaviour of the period function of the center at the point (1,1) of the planar differential system {u' = up(1−vq),v'= μvq(up−1), where p, q, μ ∈ R with pq > 0 and μ > 0. [...]
2010 -  10.1016/j.amc.2010.03.025
Applied Mathematics and Computation, Vol. 216, Issue 7 (June 2010) , p. 1956-1964
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Differential equations with a given set of solutions
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ;
Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z(t),…,z(t)}, with z(t)=x(t)+iy(t) and z¯(t)=x(t)−iy(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z,z¯)=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.
2020 - 10.1016/j.amc.2019.124659
Applied Mathematics and Computation, Vol. 365 (January 2020) , art. 124659
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31 p, 10.1 MB |
Trapezoid central configurations
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Corbera Subirana, Montserrat (Universitat de Vic. Departament d'Enginyeries) ;
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Pérez-Chavela, Ernesto (UAM-Iztapalapa(México). Departamento de Matemáticas)
We classify all planar four-body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four-body trapezoid central configurations with positive masses forms a two-dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. [...]
2019 - 10.1016/j.amc.2018.10.066
Applied Mathematics and Computation, Vol. 346 (April 2019) , p. 127-142
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13 p, 906.5 KB |
Newton's method for symmetric quartic polynomials
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Campos, Beatriz (Universitat Jaume I(Castelló de la Plana). Departament de Matemàtiques) ;
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ;
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ;
Vindel, Pura (Universitat Jaume I(Castelló de la Plana). Departament de Matemàtiques)
We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials p_a,b(z)=z^4 az^3 bz^2 az 1, where a and b are real parameters. We divide the parameter plane (a,b) R^2 into twelve open and connected regions where p, p' and p'' have simple roots. [...]
2016 - 10.1016/j.amc.2016.06.021
Applied Mathematics and Computation, Vol. 290 (2016) , p. 326-335
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21 p, 834.7 KB |
Centers for a class of generalized quintic polynomial differential systems
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Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We classify the centers of the polynomial differential systems in R2 of degree d ≥ 5 odd that in complex notation writes as z˙ = iz + (zz¯)d−5/2 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5), where A, B, C, D, E, F ∈ C and either A = Re(D) = 0, or A = Im(D) = 0, or Re(A) = D = 0, or Im(A) = D = 0.
2014 - 10.1016/j.amc.2014.05.047
Applied Mathematics and Computation, Vol. 242 (2014) , p. 187-195
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