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Articles, 45 registres trobats
Documents de recerca, 3 registres trobats
Articles 45 registres trobats  1 - 10següentfinal  anar al registre:
1.
7 p, 289.4 KB Limit cycles of a second-order differential equation / Chen, Ting (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide an upper for the maximum number of limit cycles bifurcating from the periodic solutions of x=0, when we perturb this system as follows \ (1 ^m )Q(x,y) x=0, \] where >0 is a small parameter, m is an arbitrary non-negative integer, Q(x,y) is a polynomial of degree n and =(y/x). [...]
2019 - 10.1016/j.aml.2018.08.015
Applied mathematics letters, Vol. 88 (2019) , p. 111-117  
2.
20 p, 447.6 KB On uniqueness of limit cycles in general Bogdanov-Takens bifurcation / Han, Maoan (Shanghai Normal University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yang, Junmin (Hebei Normal University. College of Mathematics and Information Science)
In this paper we present a complete study to the well-known Bogdanov-Takens bifurcation and give a rigorous proof for the uniqueness of limit cycles.
2018 - 10.1142/S0218127418501158
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, No. 9 (2018) , art. 1850115  
3.
15 p, 343.1 KB Algebraic limit cycles in piecewise linear differential systems / Buzzi, Claudio A. (Universidade Estadual Paulista (Brasil). Department of Mathematics) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some 1-parameter families with a saddle-node bifurcation of algebraic limit cycles. [...]
2018 - 10.1142/S0218127418500396
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, No. 3 (2018) , art. 1850039  
4.
38 p, 502.2 KB Limit cycles via higher order perturbations for some piecewise differential systems / Buzzi, Claudio A. (Universidade Estadual Paulista (Brasil). Department of Mathematics) ; Lima, Mauricio Firmino Silva (Universidade Federal do ABC(Brazil). Centro de Matemática Computacâo e Cognicâo) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x',y')=(-y + εf(x,y,ε),x εg(x,y,ε)). In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. [...]
2018 - 10.1016/j.physd.2018.01.007
Physica D. Nonlinear phenomena, Vol. 371 (May 2018) , p. 28-47  
5.
14 p, 356.4 KB Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles.
2018 - 10.1016/j.jmaa.2018.07.024
Journal of mathematical analysis and applications, Vol. 467, issue 1 (Nov. 2018) , p. 537-549  
6.
10 p, 567.6 KB On the Bifurcation of Limit Cycles Due to Polynomial Perturbations of Hamiltonian Centers / Colak, Ilker (Drexel University (Texas). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We study the number of limit cycles bifurcating from the peri- od annulus of a real planar polynomial Hamiltonian ordinary differential system with a center at the origin when it is perturbed in the class of polynomial vector fields of a given degree.
2017 - 10.1007/s00009-017-0857-2
Mediterranean Journal of Mathematics, 2017  
7.
16 p, 437.4 KB Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory / Benterki, Rebiha (Centre Universitaire de Bordj Bou Arréridj(Algeria). Département de Mathématiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.
2017 - 10.1016/j.cam.2016.08.047
Journal of Computational and Applied Mathematics, Vol. 313 (2017) , p. 273-283  
8.
18 p, 599.5 KB When parallels and meridians are limit cycles for polynomial vector fields on quadrics of revolution in the euclidean 3-space / Dias, Fabio Scalco (Universidade Federal de Itajubá(Brazil). Instituto de Matemática e Computacâo) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá(Brazil). Instituto de Matemática e Computacâo)
We study polynomial vector fields of arbitrary degree in R^3 with an invariant quadric of revolution. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. [...]
2016 - 10.1142/S0218127416501601
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 26 Núm. 9 (2016) , p. 1650160 (14 pages)  
9.
30 p, 812.6 KB Averaging methods of arbitrary order, periodic solutions and integrability / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Wu, Kesheng (Shanghai Jiao Tong University. Department of Mathematics) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential systems, and it unifies many different kinds of averaging methods. [...]
2016 - 10.1016/j.jde.2015.11.005
Journal of Differential Equations, Vol. 260 (2016) , p. 4130-4156  
10.
13 p, 615.6 KB Limit cycles of linear vectors on manifolds / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.
2016
Nonlinearity, Vol. 29 (2016) , p. 3120-3131  

Articles : 45 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 3 registres trobats  
1.
93 p, 9.8 MB Putting the cycle back into business cycle analysis / Beaudry, Paul ; Galizia, Dana ; Portier, Franck
Are business cycles mainly a response to persistent exogenous shocks, or do they instead reflect a strong endogenous mechanism which produces recurrent boom-bust phenomena? In this paper we present new evidence in favour of the second interpretation and, most importantly, we highlight the set of key elements that influence our answer to this question. [...]
The ADEMU Working Paper Series is being supported by the European Commission Horizon 2020 European Union funding for Research & Innovation, grant agreement No 649396.

2018 (ADEMU Working Paper Series ; 92)  
2.
52 p, 988.3 KB Is the macroeconomy locally unstable and why should we care? / Beaudry, Paul ; Galizia, Dana ; Portier, Franck
In most modern macroeconomic models, the steady state (or balanced growth path) of the system is a local attractor, in the sense that, in the absence of shocks, the economy would converge to the steady state. [...]
The ADEMU Working Paper Series is being supported by the European Commission Horizon 2020 European Union funding for Research & Innovation, grant agreement No 649396.

2016 (ADEMU Working Paper Series ; 34)  
3.
143 p, 889.1 KB Uniform isochronous centers of degrees 3 and 4 and their perturbations / Itikawa, Jackson ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En este trabajo se estudian los sistemas diferenciales polinomiales planos de grado 3 y 4 con un centro isócrono uniforme. Proporcionamos una clasificación para estos sistemas con respecto a la equivalencia topológica de sus retratos de fase globales en el disco de Poincaré. [...]
[Barcelona] : Universitat Autònoma de Barcelona, 2015  

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