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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
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2026-10-05
10:57
36 p, 564.1 KB An SIS Model with Importation and Removal / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zeng, Hui (Sun Yat-sen University. School of Mathematics)
The Susceptible-Infectious-Susceptible (SIS) model is a classical model for describing the spread of diseases without permanent immunity and has been studied by many authors. In this paper, we characterize all topologically distinct phase portraits in the Poincaré disc for a particular SIS epidemic model with a constant importation or removal rate of infected individuals. [...]
2026 - 10.1142/S0218127426502238
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 36, Num. 16 (December 2026) , art. 2650223  
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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  
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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  
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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  
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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  
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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  
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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  
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2026-10-02
16:12
18 p, 1.2 MB The dynamics of the Ehrhard-Müller system with invariant algebraic surfaces / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rondon Vielma, Gabriel Alexis (Universidade Federal de Minas Gerais. Instituto de Ciências Exatas. Departamento de Matemática)
In this paper we study the global dynamics of the Ehrhard-Müller differential system ˙ x = s(y−x), ˙y = rx − xz −y + c, ˙z = x y−z, where s, r and c are real parameters, and x, y, and z are real variables. [...]
2026 - 10.1063/5.0281236
Journal of mathematical physics, Vol. 67, Num. 8 (August 2026) , art. 082701  
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2026-10-02
16:12
13 p, 364.8 KB Hopf bifurcation in Kolmogorov systems of degree 4 in R2 and R3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática)
We consider the Kolmogorov system of degree 4 in R 2 having an equilibrium point in the positive quadrant and the Kolmogorov system of degree 4 in R 3 having an equilibrium point in the positive octant. [...]
2025 - 10.1063/5.0275638
Journal of mathematical physics, Vol. 66, Num. 12 (December 2025) , art. 122709  
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2026-10-02
17:52
31 p, 3.0 MB Dynamics for a Rayleigh-Liénard-Duffing oscillator in wing rock / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Data Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Haishan (Guangdong University of Finance and Economics. School of Statistics and Data Science)
During the past few decades there has been significant scholarly interest in the investigation of piecewise differential systems, primarily because these systems facilitate the modeling of various complex phenomena. [...]
2026 - 10.1063/5.0267733
Journal of mathematical physics, Vol. 67, Num. 3 (March 2026) , art. 032703  
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