UAB Digital Repository of Documents 14 records found  1 - 10next  jump to record: Search took 0.02 seconds. 
1.
33 p, 10.7 MB Periodic orbits of perturbed non-axially symmetric potentials in 1:1:1 and 1:1:2 resonances / Corbera Subirana, Montserrat (Universitat de Vic. Departament d'Enginyeries) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
2018 - 10.3934/dcdsb.2018101
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 6 (Aug. 2018) , p. 2299-2337  
2.
13 p, 709.8 KB Algebraic limit cycles for quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We prove that for a quadratic polynomial differential system having three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, has at most one algebraic limit cycle. [...]
2018 - 10.3934/dcdsb.2018070
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 6 (2018) , p. 2475-2485  
3.
36 p, 1.2 MB Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martinez Mancilla, Yohanna Paulina (Universidad del Bío-Bío. Departamento de Matemática) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
We provide normal forms and the phase portraits in the Poincaré disk for all the linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis.
2018 - 10.3934/dcdsb.2018047
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 2 (2018) , p. 887-912  
4.
15 p, 328.5 KB Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems / Chen, Xingwu (Sichuan University (Xina). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)
It is well known that the cyclicity of a Hopf bifurcation in continuous quadratic polynomial differential systems in \R^2 is 3. In contrast here we consider discontinuous differential systems in \R^2 defined in two half--planes separated by a straight line. [...]
2017 - 10.3934/dcdsb.2017203
Discrete and Continuous Dynamical Systems. Series B, Vol. 22 Núm. 10 (2017) , p. 3953-3965  
5.
7 p, 266.0 KB Periodic solutions of some classes of continuous second-order differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba (Algèria). Department of Mathematics)
We study the periodic solutions of the second--order differential equations of the form x x^n = f(t), or x.
2017 - 10.3934/dcdsb.2017022
Discrete and Continuous Dynamical Systems. Series B, Vol. 22 Núm. 2 (2017) , p. 477-482  
6.
9 p, 334.3 KB Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bio Bio (Chile). Departamento de Matemática)
A ratio–dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E ∗ at the positive octant is unstable. [...]
2016 - 10.3934/dcdsb.2016026
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 6 (2016) , p. 1859-1867  
7.
17 p, 333.9 KB On the analytic integrability of the Liénard analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We consider the Liénard analytic differential systems x = y, y =-g(x) -f(x)y, where f,g: R R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals.
2016 - 10.3934/dcdsb.2016.21.557
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 2 (2016) , p. 557-573  
8.
13 p, 310.1 KB Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. [...]
2016 - 10.3934/dcdsb.2016.21.121
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 1 (2016) , p. 121-131  
9.
6 p, 641.7 KB Analytic integrability of a class of planar polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
In this paper we find necessary and sufficient conditions in order that the differential systems of the form ˙x = xf(y), ˙y = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. [...]
2015 - 10.3934/dcdsb.2015.20.2657
Discrete and Continuous Dynamical Systems. Series B, Vol. 20 Núm. 8 (2015) , p. 2657-2661  
10.
10 p, 718.0 KB On the limit cycles of the Floquet differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rodrigues, Ana (Universidade do Porto(Portugal). Centro de Matemática)
We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x˙(t) = Ax(t) + ε(B(t)x(t)+b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n×n matrices, the components of b(t) and B(t) are T–periodic functions, the differential equation x˙(t) = Ax(t) has a plane filled with T–periodic orbits, and ε is a small parameter. [...]
2014 - 10.3934/dcdsb.2014.19.1129
Discrete and Continuous Dynamical Systems. Series B, Vol. 19 Núm. 4 (2014) , p. 1129-1136  

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