UAB Digital Repository of Documents 19 records found  1 - 10next  jump to record: Search took 0.01 seconds. 
1.
12 p, 296.1 KB Piecewise linear differential systems with only centers can create limit cycles? / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
In this article, we study the continuous and discontinuous planar piecewise differential systems formed only by linear centers separated by one or two parallel straight lines. When these piecewise differential systems are continuous, they have no limit cycles. [...]
2018 - 10.1007/s11071-017-3866-6
Nonlinear dynamics, Vol. 91, issue 1 (Jan. 2018) , p. 249-255  
2.
13 p, 712.8 KB Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension / Barreira, Luis (Instituto Superior Técnico (Portugal). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We study the limit cycles which can bifurcate from a zero--Hopf singularity of a C^m 1 differential system in \R^n, i. e. from a singularity with eigenvalues b i and n-2 zeros for n 3. If this singularity is at the origin of coordinates and the Taylor expansion of the differential system at the origin without taking into account the linear terms starts with terms of order m, from the origin it can bifurcate s limit cycles with s \ 0,1, 2^n-3\ if m=2 (see LZ), with s \ 0,1, 3^n-2\ if m=3, with s 6^n-2 if m=4, and with s 4 5^n-2 if m=5. [...]
2018 - 10.1007/s11071-018-4115-3
Nonlinear dynamics, Vol. 92, issue 3 (May 2018) , p. 1159-1166  
3.
30 p, 1.1 MB Global dynamics of a SD oscillator / Chen, Hebai (Fuzhou University. College of Mathematics and Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences)
In this paper we derive the global bifurcation diagrams of a SD oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter a. We research all possible bifurcations of this system, including Pitchfork bifurcation, degenerate Hopf bifurcation, Homoclinic bifurcation, Double limit cycle bifurcation, Bautin bifurcation and Bogdanov-Takens bifurcation. [...]
2018 - 10.1007/s11071-017-3979-y
Nonlinear dynamics, Vol. 91, issue 3 (Feb. 2018) , p. 1755-1777  
4.
16 p, 3.3 MB The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems / Castillo, Juan (Universidad de Sonora (Mèxic). Departamento de Matemáticas) ; Verduzco, Fernando (Universidad de Sonora (Mèxic). Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.
2017 - 10.1007/s11071-017-3766-9
Nonlinear Dynamics, Vol. 90 (2017) , p. 1829-1840  
5.
10 p, 312.5 KB Transcritical and zero-Hopf bifurcations in the Genesio system / Cardin, Pedro Toniol (Universidade Estadual Paulista (Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the existence of transcritical and zero--Hopf bifurcations of the third--order ordinary differential equation a b c x - x^2 = 0, called the Genesio equation, which has a unique quadratic nonlinear term and three real parameters. [...]
2017 - 10.1007/s11071-016-3259-2
Nonlinear Dynamics, Vol. 88 (2017) , p. 547-553  
6.
13 p, 346.6 KB Piecewise linear differential systems without equilibria produce limit cycles? / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
In this article we study the planar piecewise differential systems formed by two linear differential systems separated by a straight line, such that both linear differential have no equilibria, neither real nor virtual.
2017 - 10.1007/s11071-016-3236-9
Nonlinear Dynamics, Vol. 88 (2017) , p. 157-164  
7.
15 p, 795.4 KB Periodic orbits of a perturbed 3–dimensional isotropic oscillator with axial symmetry / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vera, Juan A. (Universidad Politécnica de Cartagena. Centro Universitario de la Defensa)
We study the periodic orbits of a generalized Yang–Mills Hamiltonian H depending on a parameter β. Playing with the parameter β we are considering extensions of the Contopoulos and of the Yang–Mills Hamiltonians in a 3-dimensional space. [...]
2015 - 10.1007/s11071-015-2371-z
Nonlinear Dynamics, Vol. 83 (2015) , p. 839-848  
8.
39 p, 790.9 KB A new approach to the vakonomic mechanics / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
The aim of this paper is to show that the Lagrange–d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the generalization of the Hamiltonian principle for nonholonomic systems with nonzero transpositional relations. [...]
2014 - 10.1007/s11071-014-1554-3
Nonlinear Dynamics, Vol. 78 (2014) , p. 2219-2247  
9.
9 p, 311.8 KB Zero-Hopf bifurcation in a hyperchaotic Lorenz system / Cid-Montiel, Lorena (Wilfrid Laurier University(Canada). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Stoica, Cristina (Wilfrid Laurier University(Canada). Department of Mathematics)
We characterize the zero–Hopf bifurcation at the singular points of a parameter co-dimension four hyperchaotic Lorenz system. Using averaging theory, we find sufficient conditions so that at the bifurcation points two periodic solutions emerge and describe the stability of these orbits.
2014 - 10.1007/s11071-013-1085-3
Nonlinear Dynamics, Vol. 75 (2014) , p. 561-566  
10.
20 p, 630.7 KB Periodic orbits for the generalized Yang-Mills Hamiltonian systems in dimension 6 / Lembarki, Fatima Ezzahra (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We apply the averaging theory to study a generalized Yang-Mills Hamiltonian system in dimension 6 with six parameters. We provide sufficient conditions on the six parameters of the system which guarantee the existence of continuous families of period orbits parameterized by the energy.
2014 - 10.1007/s11071-014-1249-9
Nonlinear Dynamics, Vol. 76 (2014) , p. 1807-1819  

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