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Graph-based problem explorer : a software tool to support algorithm design learning while solving the salesperson problem
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Hernàndez i Sabaté, Aura (Universitat Autònoma de Barcelona. Departament de Ciències de la Computació) ;
Albarracín Gordo, Lluís (Universitat Autònoma de Barcelona. Departament de Didàctica de la Matemàtica i de les Ciències Experimentals) ;
Sánchez Pujadas, Francisco Javier (Universitat Autònoma de Barcelona. Departament de Ciències de la Computació)
In this article, we present a sequence of activities in the form of a project in order to promote learning on design and analysis of algorithms. The project is based on the resolution of a real problem, the salesperson problem, and it is theoretically grounded on the fundamentals of mathematical modelling. [...]
2020 -  10.3390/math8091595
Mathematics, Vol. 8, núm. 9 (2020) , p. e1595
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30 p, 951.8 KB |
On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems
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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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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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14 p, 290.3 KB |
On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
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Han, Maoan (Shanghai Normal University. Department of Mathematics (China)) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Tian, Yun (Shanghai Normal University. Department of Mathematics (China))
Here we study the Lotka-Volterra systems in R3, i. e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. [...]
2020 - 10.3390/math8071137
Mathematics, Vol. 8, Issue 7 (July 2020) , art. 1137
2 documents
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Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
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Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellipse, they can have at most three crossing limit cycles. [...]
2020 - 10.3390/MATH8050755
Mathematics, Vol. 8, Issue 5 (May 2020) , art. 755
2 documents
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10 p, 652.9 KB |
Limit cycles for a class of third-order differential equations
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Yu, Jiang (Shanghai Jiaotong University. Department of Mathematics (China)) ;
Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics (China))
In this paper we study the limit cycles of the third-order differential equation . . . x − μẍ + ẋ − μx = εF(x, ẋ , ẍ, t) where μ ≠ 0, ε is small enough and F Є C2 is a 2π-periodic function of variable t.
2010 - 10.1216/RMJ-2010-40-2-581
The Rocky Mountain Journal of Mathematics, Vol. 40, Issue 2 (2010) , p. 581-594
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On Poncelet's maps
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Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
Given two ellipses, one surrounding the other one, Poncelet introduced a map P from the exterior one to itself by using the tangent lines to the interior ellipse. This procedure can be extended to any two smooth, nested and convex ovals and we call these types of maps, Poncelet's maps. [...]
2010 - 10.1016/j.camwa.2010.06.027
Computers and Mathematics with Applications, Vol. 60, Issue 5 (September 2010) , p. 1457-1464
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