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Articles 19 records found  1 - 10next  jump to record:
1.
13 p, 369.7 KB Dynamics of the Higgins-Selkov and Selkov systems / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We describe the global dynamics in the Poincaré disc of the Higgins--Selkov model * x'= k₀-k₁xy², y'= k₂y+ k₁xy², * where k₀,k₁,k₂ are positive parameters, and of the Selkov model x'= -x+ay+x²y, y'= b-ay-x²y, * where a,b are positive parameters.
2018 - 10.1016/j.chaos.2018.07.007
Chaos, solitons and fractals, Vol. 114 (Sep. 2018) , p. 145-150  
2.
9 p, 291.9 KB On the global dynamics of a finance model / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matematica)
Recently several works have studied the following model of finance \[ x= z (y-a) x, y= 1-b y -x^2, z= -x -c z, \] where a, b and c are positive real parameters. We study the global dynamics of this polynomial differential system, and in particular for a one--dimensional parametric subfamily we show that there is an equilibrium point which is a global attractor.
2018 - 10.1016/j.chaos.2017.10.026
Chaos, solitons and fractals, Vol. 106 (2018) , p. 1-4  
3.
15 p, 651.1 KB Centers of weight-homogeneous polynomial vector fields on the plane / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We characterize all centers of a planar weight-homogeneous polynomial vector fields. Moreover we classify all centers of a planar weight-homogeneous polynomial vector fields of degrees 6 and 7.
2017
Proceedings of the American Mathematical Society, Vol. 145 Núm. 6 (2017) , p. 2539-2555  
4.
14 p, 310.6 KB On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. [...]
2017 - 10.1007/s11040-017-9240-6
Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics, Vol. 20 Núm. 2 (2017) , p. 1-12  
5.
11 p, 650.3 KB Global dynamics of the Kummer-Schwarz differential equation / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bio Bio(Chile). Departamento de Matemática)
This paper studies the Kummer–Schwarz differential equation 2 ˙x. . . x −3¨x2 = 0 which is of special interest due to its relationship with the Schwarzian derivative. This differential equation is transformed into a first order differential system in R3, and we provide a complete description of its global dynamics adding the infinity.
2014 - 10.1007/s00009-013-0299-4
Mediterranean Journal of Mathematics, Vol. 11 (2014) , p. 477-486  
6.
21 p, 642.5 KB Phase portraits of quadratic Lotka-Volterra systems with a Darboux invariant in the Poincaré disc / Bolaños Rivera, Yudi Marcela (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the global phase portraits in the Poincaré disc of all the planar Lotka–Volterra quadratic polynomial differential systems having a Darboux invariant.
2014 - 10.1142/S0219199713500417
Communications in Contemporaray Mathematics, Vol. 16 Núm. 6 (2014) , p. 1350041 (23 pages)  
7.
21 p, 515.2 KB Global dynamics of the Benoît system / Lima, Mauricio Firmino Silva (Universidade Federal do ABC(Brazil). Centro de Matemática Computacâo e Cognicâo) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we work with a two-degree polynomial differential system in R3 related with the canard phenomena. We show that this system is completely integrable, and we provide its global phase portrait in the Poincaré ball using the Poincaré-Lyapunov compactification.
2014 - 10.1007/s10231-012-0318-2
Annali di Matematica Pura ed Applicata, Vol. 193 Núm. 4 (2014) , p. 1103-1122  
8.
62 p, 2.4 MB Geometric configurations of singularities for quadratic differential systems with total finite multiplicity m_f=2 / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [3]. [...]
2014
Electronic Journal of Differential Equations, Vol. 2014 Núm. 159 (2014) , p. 1-79  
9.
35 p, 1.6 MB Global configurations of singularities for quadratic differential systems with total finite multiplicity three and at most two real singularities / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In this work we consider the problem of classifying all configurations of singularities, finite and infinite, of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. [...]
2014 - 10.1007/s12346-014-0119-7
Qualitative Theory of Dynamical Systems, Vol. 13 (2014) , p. 305-351  
10.
36 p, 1.5 MB Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rezende, Alex C. (Universidade de São Paulo) ; Schlomiuk, Dana (Université de Montréal) ; Vulpe, Nicolae (Academy of Science of Moldova)
In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. [...]
2014 - 10.14232/ejqtde.2014.1.60
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 60 (2014) , p. 1-43  

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