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1.
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  
2.
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  
3.
19 p, 446.4 KB On Poincaré–Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields / Buzzi, Claudio Aguinaldo (Universidade Estadual Paulista(Brazil). Departamento de Matemática) ; de Carvalho, Tiago (Universidade Estadual Paulista(Brazil). Departamento de Matemática) ; Euzébio, Rodrigo D. (Universidade Estadual Paulista (Brasil). Departamento de Matemática)
In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. A Poincaré–Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov systems not predicted in classical Poincaré–Bendixson theory and whose interior is non-empty is exhibited. [...]
2018 - 10.5565/PUBLMAT6211806
Publicacions matemàtiques, Vol. 62 Núm. 1 (2018) , p. 113-131 (Articles)  
4.
30 p, 478.1 KB Center boundaries for planar piecewise-smooth differential equations with two zones / Buzzi, Claudio A. (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  
5.
6 p, 542.7 KB On the periodic solutions of the static, spherically symmetric Einstein-Yang-Mills equations / Buzzi, Claudio Aguinaldo (Universidade Estadual Paulista(Brazil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that the static, spherically symmetric Einstein-Yang-Mills equations do not have periodic solutions.
2012 - 10.1063/1.4770046
Journal of Mathematical Physics, Vol. 53 (2012) , p. 122703  
6.
18 p, 411.1 KB Piecewise linear perturbations of a linear center / Buzzi, Claudio Aguinaldo (Universidade Estadual Paulista(Brazil). Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pessoa, Claudio (Universidade Estadual Paulista(Brazil). Departamento de Matemática)
This paper is mainly devoted to study the limit cycles that can bifurcate from a linear center using a piecewise linear perturbation in two zones. We consider the case when the two zones are separated by a straight line Σ and the singular point of the unperturbed system is in Σ. [...]
2013 - 10.3934/dcds.2013.33.3915
Discrete and continuous dynamical systems. Series A, Vol. 33 Núm. 9 (2013) , p. 3915-3936  
7.
6 p, 508.3 KB Discussion on the limit cycles of the Lev Ginzburg equation by M. Bellamy and R.E. Mickens / Buzzi, Claudio Aguinaldo (Universidade Estadual Paulista "Julio de Mesquita Filho". Departamento de Matemática) ; Donizete Euzébio, Rodrigo (Universidade Estadual Paulista "Julio de Mesquita Filho". Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá. Instituto de Ciências Exactas)
2012 - 10.1016/j.jsv.2012.07.008
Journal of Sound and Vibration, Vol. 331 (2012) , p. 5168-5170  
8.
7 p, 269.1 KB On the limit cycles of a class of piecewise linear differential systems in R^4 with two zones / Buzzi, Claudio Aguinaldo (Universidade Federal de Goias. Instituto de Matematica e Estatística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (Universidade Federal de Goias. Instituto de Matematica e Estatística)
We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems with two zones. Our main result shows that three is an upper bound for the number of limit cycles that bifurcate from a center, up to first order expansion of the displacement function. [...]
2011 - 10.1016/j.matcom.2011.08.006
Mathematics and computers in simulation, Vol. 82 (2011) , p. 533-539  
9.
11 p, 324.2 KB No periodic orbits for the type A Bianchi's systems / Buzzi, Claudio Aguinaldo (Departamento de Matemática – IBILCE–UNESP) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that all the type A Bianchi's systems do not have periodic solutions.
2015 - 10.1080/14029251.2015.1023561
Journal of Nonlinear Mathematical Physics, Vol. 22 Núm. 2 (2015) , p. 170-179  
10.
13 p, 527.5 KB Hopf bifurcation in the full repressilator equations / Buzzi, Claudio Aguinaldo (IBILCE–UNESP (Brazil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we prove that the full repressilator equations, in dimension six undergo a supercritical Hopf bifurcation.
2015 - 10.1002/MMA.3158
Mathematical Methods in the Applied Sciences, Vol. 38 (2015) , p. 1428-1436  

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8 Buzzi, Claudio Aguinaldo
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