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Articles, 13 registres trobats
Articles 13 registres trobats  1 - 10següent  anar al registre:
1.
23 p, 764.3 KB Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields / Cardoso, Joäo L. (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matematica (Brazil)) ; Tonon, Durval José (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil))
In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. [...]
2020 - 10.1080/14689367.2020.1722064
Dynamical Systems, vol. 35 3 (February 2020) p. 490-514  
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2.
19 p, 441.0 KB Limit cycles in 4-star-symmetric planar piecewise linear systems / Buzzi, Claudio (Universidade Estadual Paulista. Departamento de Matemática (Brazil)) ; Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil)) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise linear vector fields on the plane when the switching curve is xy=0. We consider the symmetric case. That is, one vector field defined in the odd quadrants and the other in the even ones. [...]
2020 - 10.1016/j.jde.2019.09.008
Journal of differential equations, Vol. 268, Issue 5 (February 2020) , p. 2414-2434  
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3.
29 p, 594.7 KB New lower bound for the Hilbert number in piecewise quadratic differential systems / Da Cruz, Leonardo Pereira Costa (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. [...]
2019 - 10.1016/j.jde.2018.09.032
Journal of differential equations, Vol. 266, Núm. 7 (March 2019) , p. 4170-4203  
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4.
15 p, 343.1 KB Algebraic limit cycles in piecewise linear differential systems / Buzzi, Claudio. (Universidade Estadual Paulista (Brasil). Department of Mathematics) ; Gasull, 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  
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5.
38 p, 502.2 KB Limit cycles via higher order perturbations for some piecewise differential systems / Buzzi, Claudio. (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  
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6.
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  
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7.
30 p, 478.1 KB Center boundaries for planar piecewise-smooth differential equations with two zones / Buzzi, Claudio. (Universidade Estadual Paulista (Brasil). Department of Mathematics) ; Pazim, Rubens (Universidade Federal de Mato Grosso (Brasil). Inst. de Ciências Naturais Humanas e Sociais) ; Pérez-González, Set (Universidade Estadual Paulista (Brasil). Department of Mathematics)
This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. [...]
2017 - 10.1016/j.jmaa.2016.07.022
Journal of mathematical analysis and applications, Vol. 445 (2017) , p. 631-649  
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8.
23 p, 386.6 KB Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática) ; Rodrigues, Camila A. B. (Universidade de São Paulo (Brasil). Departamento de Matemática)
2017 - 10.1016/j.physd.2017.05.003
Physica D. Nonlinear phenomena, Vol. 353-354 (2017) , p. 1-10  
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9.
12 p, 272.4 KB Piecewise linear differential systems with two real saddles / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (Universidade Federal de Goiás(Brazil).Instituto de Matemática e Estatística) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a generalized singular point on the line. [...]
2013 - 10.1016/j.matcom.2013.02.007
Mathematics and computers in simulation, Vol. 95 (2013) , p. 13-22  
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10.
14 p, 377.1 KB Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
In this paper we study the maximum number of limit cycles for planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here we only consider non-sliding limit cycles. [...]
2013 - 10.1142/S0218127413500661
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 4 (2013) , p. 1350066 (10 pages)  
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Articles : 13 registres trobats   1 - 10següent  anar al registre:
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