UAB Digital Repository of Documents 16 records found  1 - 10next  jump to record: Search took 0.01 seconds. 
1.
19 p, 420.8 KB Phase portraits of continuous piecewise linear Liénard differential systems with three zones / Li, Shimin (Guangdong University of Finance and Economics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. [...]
2019 - 10.1016/j.chaos.2018.12.037
Chaos, solitons and fractals, Vol. 120 (March 2019) , p. 149-157  
2.
10 p, 613.0 KB Final evolutions for simplified multistrain/two-stream model for tuberculosis and dengue fever / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de São Paulo. Departamento de Matemática) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
The simplified multistrain/two-stream model for the tuberculosis and the Dengue fever here considered has three compartments, one susceptible and the other two infectious. We characterize all the final evolutions of this model under generic assumptions.
2019 - 10.1016/j.chaos.2018.11.022
Chaos, solitons and fractals, Vol. 118 (January 2019) , p. 181-186  
3.
10 p, 627.7 KB Periodic solutions and their stability of some higher-order positively homogenous differential equations / Cen, Xiuli (Sun Yat-sen University(China). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Meirong (Tsinghua University. Department of Mathematical Sciences)
In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x^(m) f_n(x) = h(t), where the integers m, n2, f_n(x)= x^n or $^ n with = 1, and h(t) is a continuous T-periodic function of non-zero average, and is a positive small parameter. [...]
2018 - 10.1016/j.chaos.2017.11.032
Chaos, solitons and fractals, Vol. 106 (Jan. 2018) , p. 285-288  
4.
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  
5.
12 p, 275.2 KB On Darboux integrability of Edelstein's reaction system in R³ / Ferragut, Antoni (Universitat Jaume I. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica) ; Wiuf, Carsten (Københavns Universitet. Department of Mathematical Sciences)
We consider Edelstein's dynamical system of three reversible reactions in R³ and show that it is not Darboux integrable. To do so we characterize its polynomial first integrals, Darboux polynomials and exponential factors.
2018 - 10.1016/j.chaos.2018.01.029
Chaos, solitons and fractals, Vol. 108 (March 2018) , p. 129-135  
6.
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  
7.
5 p, 574.4 KB Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. [...]
2017 - 10.1016/j.chaos.2017.01.014
Chaos, Solitons and Fractals, Vol. 96 (2017) , p. 130-131  
8.
12 p, 1.7 MB New families of periodic orbits for a galactic potential / de Bustos, Maria T. (Universidad de Salamanca. Departamento de Matemática Aplicada) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Vera, Juan A. (Universidad Politécnica de Cartagena. Centro Universitario de la Defensa)
The Hamiltonian system associated to the Hamiltonian \[ H=(P_1^2 P_2^2 P_3^2)/2 (Q_1^2 Q_2^2 Q_3^2)/2 (Q_1^4 Q_2^4 Q_3^4 a(Q_1^2Q_2^2 Q_1^2Q_3^2 Q_2^2Q_3^2)), \] where and a are parameters and is small, describes the local motion in the central area of a galaxy. [...]
2016 - 10.1016/j.chaos.2015.11.003
Chaos, Solitons and Fractals, Vol. 82 (2016) , p. 97-102  
9.
13 p, 292.9 KB On the Darboux integrability of a cubic CRNT model in R^5 / Ferragut, Antoni (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Darboux integrability of a differential system with parameters coming from a chemical reaction model in R5. We find all its Darboux polynomials and exponential factors and we prove that it is not Darboux integrable.
2016 - 10.1016/j.chaos.2015.11.011
Chaos, Solitons and Fractals, Vol. 82 (2016) , p. 131-138  
10.
8 p, 872.5 KB Zero-Hopf bifurcation in the generalized Michelson system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba(Algeria). Department of Mathematics)
We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential system x ̇ =y, y ̇ =z, z ̇ =a by cz−x^2/2, where a, b and c are real arbitrary parameters. [...]
2016 - 10.1016/j.chaos.2015.11.013
Chaos, Solitons and Fractals, Vol. 89 (2016) , p. 228-231  

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