Página principal > Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
GSD (Grupo de Sistemas Dinámicos)

Los sistemas dinámicos son, y siempre han sido, una de las principales líneas de investigación en Matemáticas. Es de interés de todas las civilizaciones humanas el comprender cuestiones importantes, como el movimiento de los planetas, la evolución de las poblaciones, o el estudio de la dinámica en sistemas deterministas, de modo que los sistemas dinámicos se han convertido en un objetivo importante de estudio. Después de muchos años de evolución, el área de los sistemas dinámicos ha sufrido varias transformaciones y ha desarrollado distintas ramas que han permitido responder preguntas de diversa índole.

Las líneas principales de investigación del Grupo de Sistemas Dinámicos de la UAB (GSD-UAB) son: Mecánica celeste, Dinámica compleja, Sistemas Dinámicos discretos y Teoría cualitativa de ecuaciones diferenciales.

Los miembros de nuestro grupo trabajan principalmente en las universidades catalanas (UAB, UB, UdG, UPC, URV, UVic), aunque algunos de nuestros investigadores trabajan en otras universidades de España y del extranjero. El GSD-UAB colabora asiduamente con varios grupos de investigación nacionales e internacionales.

Página web: http://www.gsd.uab.cat
Estadísticas de uso Los más consultados
Buscar en 1,352 registros por:
Consejos para la búsqueda
Búsqueda avanzada
Últimas adquisiciones:
2026-09-30
17:43
25 p, 1.1 MB The codimension of the phase portraits for degenerate quadratic differential systems / Artés, Joan C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulp, Nicolae (Moldova State University. Institute of Mathematics and Computer Science)
In this paper we present a complete study of degenerate quadratic differential systems, i. e. the polynomials from right-hand sides of these systems are not co-prime. We give the complete set of their phase portraits together with the necessary and sufficient conditions for the realization of each one of them. [...]
2024 - 10.56415/basm.y2024.i3.p29
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica., Vol. 106, Num. 3 (2024) , p. 29-53  
Registro completo - Creative Commons
2026-09-30
19:40
18 p, 358.1 KB Centers of cubic polynomial differential systems / Anacona, Gerardo H. (Federal University of Goiás. Institute of Mathematics and Statistics) ; De Freitas, Bruno R. (Federal University of Goiás. Institute of Mathematics and Statistics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
An equilibrium point p of a differential system in the plane R2 is a center if there exists a neighborhood U of p such that U \{p} is filled with periodic orbits. A difficult classical problem in the qualitative theory of differential systems in the plane is the problem of distinguishing between a focus and a center. [...]
2025 - 10.3934/cpaa.2025072
Communications on pure & applied analysis, Vol. 24, Num. 11 (November 2025) , p. 2130-2145  
Registro completo -
2026-09-30
19:40
12 p, 444.4 KB Periodic Solutions for Two Classes of Duffing Differential Equations via Averaging Theory∗ / Rabia, Afef Amina (Badji Mokhtar-Annaba University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (Badji Mokhtar-Annaba University. Department of Mathematics)
The aim of this paper is to present sufficient conditions for the existence of periodic solutions in two classes of Duffing differential equations. While previous studies have focused on numerical results for these equations, this paper offers new analytical findings using averaging theory. [...]
2026 - 10.12150/jnma.2026.648
Journal of Nonlinear Modeling and Analysis, Vol. 8, Num. 3 (June 2026) , p. 648-659  
Registro completo -
2026-09-30
20:26
113 p, 6.4 MB Quadratic Differential Systems with a Weak Focus of First-Order and a Finite Saddle-Node / Artés, Joan C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Trullàs Fernández, Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than 1000 papers were written on these systems, a complete understanding of this class is still missing. [...]
2026 - 10.1142/S0218127426300132
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 36, Num. 6 (May 2026) , art. 2630013  
Registro completo - Creative Commons
2026-09-30
21:13
7 p, 408.8 KB The Simplest Polynomial Differential Systems in ℝ3 Having an Invariant Sphere / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Until now all the examples of polynomial differential systems in (Formula presented. ) exhibiting an invariant sphere have degree larger than one. In this note we show, for the first time, that the polynomial differential systems in (Formula presented. [...]
2025 - 10.1080/00029890.2025.2558310
American Mathematical Monthly, Vol. 132, Num. 10 (October 2025) , p. 1023-1029  
Registro completo - Creative Commons
2026-09-30
21:13
11 p, 1016.3 KB Reverse Newhouse-Ruelle-Takens route to chaos and time-dependent Hamiltonian formulation of a generalized Muthuswamy-Chua system / Muthuswamy, Bharathwaj (Nonlinear Engineering Research and Development Inc. (USA)) ; Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon) ; Concas, Roberto (Istituto Nazionale di Ricerca Metrologica) ; Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Chua, Leon O. (University of California - Berkeley. Department of EECS)
This work introduces a generalization of the Muthuswamy-Chua system of equations. The generalization allows us to embed memristive/hysteretic systems in a time-varying Hamiltonian, which acts as an energy-like Lyapunov function, whose growth or decay is governed by the memristor feedback and by whether the oscillator is momentarily kinetic- or potential-dominated. [...]
2026 - 10.1063/5.0304010
Chaos, Vol. 36, Num. 1 (January 2026) , art. 013132  
Registro completo -
2026-07-01
14:14
54 p, 2.6 MB Quadratic systems with two invariant real straight lines and an invariant parabola / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ou, Huaxin (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
After the linear differential systems in the plane the easiest ones are the quadratic polynomial differential systems. Due to their nonlinearity and also to their many applications these systems have been studied by many authors. [...]
2025 - 10.14232/ejqtde.2025.1.66
Electronic Journal of Qualitative Theory of Differential Equations, Num. 66 (2025) , p. 1-54  
Registro completo - Creative Commons
2026-07-01
13:17
49 p, 8.6 MB Phase Portraits of (2;1) Reversible Vector Fields of Low Codimension / Buzzi, Claudio (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas) ; Llibre, Jaume (Universitat Autònoma de Barcelona) ; Santana, Paulo Henrique Reis (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)
In this paper we study the phase portraits and bifurcation diagram of the symmetric singularities of codimensions zero, one and two of planar reversible vector fields having a line of reversibility.
2026 - 10.1007/s12591-026-00756-2
Differential Equations and Dynamical Systems, March 2026  
Registro completo - Creative Commons
2026-06-30
20:12
13 p, 484.2 KB From Generalized Controlled Nonlinear Oscillators to Lorenz-Like Systems / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Aix Marseille University. Université de Toulon) ; Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Chen, Guanrong (City University of Hong Kong. Department of Electrical Engineering) ; Chua, Leon O. (University of California. Department of Electrical Engineering and Computer Sciences)
Damped and driven oscillators are generally modeled with a nonautonomous second-order nonlinear ordinary differential equation including a sinusoidal driving forcing term, such as the forced Duffing equation and the forced Holmes-Rand equation. [...]
2026 - 10.1142/S0218127426300223
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 36, Num. 10 (August 2026) , art. 2630022  
Registro completo -
2026-06-25
21:12
11 p, 375.2 KB Periodic orbits of two particular classes of planar continuous piecewise linear differential systems with three zones separated by two parallel straight lines / Fonseca, A. F. (Universidade Federal de Itajubá. Instituto de Matemática e Computação) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
We study the existence and non-existence of periodic orbits in the planar continuous piecewise linear differential systems with three zones separated by two parallel straight lines. First with the additional hypothesis that the three vector fields have no equilibrium points neither real nor virtual we prove that these differential systems have no periodic orbits. [...]
2026 - 10.1007/s40590-026-00903-3
Boletin de la Sociedad Matematica Mexicana, Vol. 32, Num. 2 (June 2026) , art. 69  
Registro completo - Creative Commons
Depósito Digital de Documentos de la UAB :: Buscar :: Enviar :: Personalizar :: Ayuda
Powered by Invenio v1.1.6
Mantenido por ddd.bib@uab.cat  :: Metadatos sujetos a:
Última actualización: 02 Oct 2026, 06:06
Colaboramos