Resultats globals: 82 registres trobats en 0.02 segons.
Articles, 77 registres trobats
Llibres i col·leccions, 2 registres trobats
Documents de recerca, 3 registres trobats
Articles 77 registres trobats  1 - 10següentfinal  anar al registre:
1.
A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, X. (Shanghai Jiao Tong University. School of Mathematical Sciences and MOE-LSC (People's Republic of China))
In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in R and of the discontinuous piecewise differential systems in R formed by two linear differential systems separated by a straight line. [...]
2021 - 10.1016/j.exmath.2020.03.001
Expositiones Mathematicae, Vol. 39, Issue 1 (March 2021) , p. 48-61  
2.
The cyclicity of the period annulus of a reversible quadratic system / Liu, Changjian (Sun Yat-sen University. School of Mathematics (China)) ; Li, Chengzhi (Peking University. School of Mathematical Sciences (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that perturbing the periodic annulus of the reversible quadratic polynomial differential system x˙ = y + ax2, y˙ = −x with a ≠ 0 inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycle, including their multiplicities. [...]
2021 - 10.1017/prm.2021.2
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, (February 2021)  
3.
Limit cycles bifurcating from a zero-Hopf equilibrium of a 3-dimensional continuous differential system / Kassa, Sara (University of Annaba. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Amar (University of Annaba. Department of Mathematics (Algeria))
A zero-Hopf equilibrium of a differential system in R3 is an equilibrium point whose linear part has eigenvalues 0 and ±ωi with ω>0. We provide necessary and sufficient conditions for the existence of two or one limit cycles bifurcating from a zero-Hopf equilibrium of the following 3-dimensional Lypschizian differential systems x˙= y, y˙= z, z˙= −a y + 3y2 − xz −b, when a=b=0. [...]
2021 - 10.1007/s40863-021-00212-9
São Paulo Journal of Mathematical Sciences, (February 2021)  
4.
Phase portraits of the Higgins-Selkov system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences (Iran))
In this paper we study the dynamics of the Higgins-Selkov system x˙=1−xyγ,y˙=αy(xyγ−1−1), where α is a real parameter and γ > 1 is an integer. We classify the phase portraits of this system for γ = 3,4,5,6, in the Poincaré disc for all the values of the parameter α. [...]
2021 - 10.3934/dcdsb.2021039
Discrete and continuous dynamical systems. Series B, Vol. 26 (2021)  
5.
Lower bounds for the local cyclicity for families of centers / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Gouveia, Luiz F. S (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we are interested on how the local cyclicity of a family of centers depends on the parameters. This fact, was pointed out in [21], to prove that there exists a family of cubic centers, labeled by CD12 31 in [25], with more local cyclicity than expected. [...]
2021 - 10.1016/j.jde.2020.11.035
Journal of differential equations, Vol. 275 (February 2021) , p. 309-331  
6.
The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the maximum number of limit cycles of some classes of discontinuous piecewise differential systems formed by two differential systems separated by a straight line, when these differential systems are linear centers or three families of cubic isochronous centers, giving rise to ten different classes of discontinuous piecewise differential systems. [...]
2020 - 10.1007/s11071-020-06045-z
Nonlinear Dynamics, Vol. 102, Issue 4 (December 2020) , p. 2453-2466  
7.
Lower bounds for the local cyclicity of centers using high order developments and parallelization / Gouveia, Luiz F. S (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. [...]
2021 - 10.1016/j.jde.2020.08.027
Journal of differential equations, Vol. 271 (January 2021) , p. 447-479  
8.
Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points / Fernandes da Fonseca, Alexander (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil))
We study the existence of limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points. In this scenario, we have shown that such systems have at most one crossing limit cycle.
2020 - 10.1142/S0218127420501576
International Journal of Bifurcation and Chaos, Vol. 30, Issue 11 (September 2020) , art. 2050157  
9.
The zero-Hopf bifurcations in the Kolmogorov systems of degree 3 in R3 / Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
In this work we study the periodic orbits which bifurcate from all zero-Hopf bifurcations that an arbitrary Kolmogorov system of degree 3 in R3 can exhibit. The main tool used is the averaging theory.
2021 - 10.1016/j.cnsns.2020.105621
Communications in nonlinear science and numerical simulation, Vol. 95 (April 2021) , art. 105621  
10.
Limit cycles bifurcating of Kolmogorov systems in R2 and in R3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Centre de Recerca Matemàtica) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
In this work we consider the Kolmogorov system of degree 3 in R2 and R3 having an equilibrium point in the positive quadrant and octant, respectively. We provide sufficient conditions in order that the equilibrium point will be a Hopf point for the planar case and a zero-Hopf point for the spatial one. [...]
2020 - 10.1016/j.cnsns.2020.105401
Communications in nonlinear science and numerical simulation, Vol. 91 (December 2020) , art. 105401  

Articles : 77 registres trobats   1 - 10següentfinal  anar al registre:
Llibres i col·leccions 2 registres trobats  
1.
4 p, 235.4 KB Localizing limit cycles : from numeric to analytical results / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Université de Tours (França). Laboratoire de Mathemátiques et Physique Théorique) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica)
This note presents the results of [4]. It deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. [...]
Cham, etc : Springer Nature Switzerland AG, cop. 2018 (Trends in mathematics. Research perspectives CRM Barcelona ; 10) - 10.1007/978-3-030-01153-6_2
Extended abstracts Summer 2016, slow-fast systems and hysteresis, theory and applications, 2015, p. 17-21  
2.
16 p, 331.6 KB Canard cycles with three breaking mechanisms / Caubergh, Magdalena (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Roussarie, Robert (Université de Bourgogne)
This article deals with relaxation oscillations from a generic balanced canard cycle Γ subject to three breaking parameters of Hopf or jump type. We prove that in a rescaled layer of Γ there bifurcate at most five relaxation oscillations.
Cham, Switzerland: Springer, 2016 (Springer Proceedings in Mathematics & Statistics ; 157) - 10.1007/978-3-319-31323-8_4
Springer Proceedings in Mathematics & Statistics, 2016, p. 61-77  

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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