Resultats globals: 10 registres trobats en 0.01 segons.
Articles, 9 registres trobats
Documents de recerca, 1 registres trobats
Articles 9 registres trobats  
1.
Non-existence, existence, and uniqueness of limit cycles for a generalization of the Van der Pol-Duffing and the Rayleigh-Duffing oscillators / Cândido, Murilo R. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We study the limit cycles of some cubic family of differential equations, containing the well-known Van der Pol-Duffing and Rayleigh-Duffing oscillators. In particular, we characterize for the class of differential systems here studied the non-existence, existence and uniqueness of limit cycles. [...]
2020 - 10.1016/j.physd.2020.132458
Physica D. Nonlinear phenomena, Vol. 407 (June 2020) , art. 132458  
2.
10 p, 627.1 KB New symmetric periodic solutions for the Maxwell-Bloch differential system / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We provide sufficient conditions for the existence of a pair of symmetric periodic solutions in the Maxwell-Bloch differential equations modeling laser systems. These periodic solutions come from a zero-Hopf bifurcation studied using recent results in averaging theory.
2019 - 10.1007/s11040-019-9313-9
Mathematical Physics, Analysis and Geometry, Vol. 22, Issue 2 (June 2019) , art. 16  
3.
15 p, 386.3 KB Invariant algebraic surfaces and hopf bifurcation of a finance model / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
Recently there are several works studying the finance model ẋ=z+x(y−a),ẏ=1−by−x2,ż=−x−cz, where a,b and c are positive parameters. The first objective of this paper is to show that this model exhibits one small-amplitude periodic solution emerging from a Hopf bifurcation at the equilibrium point (0, 1/b, 0) and in the second one we show that this system does not have invariant algebraic surfaces for any value of the parameters.
2018 - 10.1142/S021812741850150X
International Journal of Bifurcation and Chaos, Vol. 28, Issue 12 (November 2018) , art. 1850150  
4.
13 p, 271.6 KB Periodic orbits bifurcating from a nonisolated zero-Hopf equilibrium of three-dimensional differential systems revisited / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilib- rium in a polynomial differential system of degree two in R³. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. [...]
2018 - 10.1142/S021812741850058X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, no. 5 (2018) , art. 1850058  
5.
29 p, 5.8 MB Zero-Hopf bifurcations in 3-dimensional differential systems with no equilibria / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We use averaging theory for studying the Hopf and zero--Hopf bifurcations in some chaotic differential systems. These differential systems have a chaotic attractor and no equilibria. Numerically we show the relation between the existence of the periodic solutions studied in these systems and their chaotic attractors.
2018 - 10.1016/j.matcom.2018.03.008
Mathematics and computers in simulation, Vol. 151 (Sep. 2018) , p. 54-76  
6.
15 p, 5.1 MB Stability of periodic orbits in the averaging theory : applications to Lorenz and Thomas' differential systems / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the kind of stability of the periodic orbits provided by higher order averaging theory. We apply these results for determining the k-hyperbolicity of some periodic orbits of the Lorenz and Thoma's differential system.
2018 - 10.1142/S0218127418300070
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, No. 3 (2018) , art. 1830007  
7.
27 p, 834.6 KB Zero-Hopf bifurcations in a hyperchaotic Lorenz system II / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently sixteen 3-dimensional differential systems exhibiting chaotic motion and having no equilibria have been studied, and it has been graphically observed that these systems have a period-doubling cascade of periodic orbits providing the route to their chaotic motions. [...]
2018
International journal of nonlinear science, Vol. 25, issue 1 (2018) , p. 3-26  
8.
31 p, 573.9 KB Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
2017 - 10.1088/1361-6544/aa7e95
Nonlinearity, Vol. 30 Núm. 9 (2017) , p. 3560-3586  
9.
12 p, 680.4 KB New results on averaging theory and applications / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i. [...]
2016 - 10.1007/s00033-016-0682-7
ZAMP. Journal of Applied Mathematics and Physics, Vol. 67:106 (2016) , p. 11  

Documents de recerca 1 registres trobats  
1.
146 p, 1.9 MB New results in averaging theory and its applications / Cândido, Murilo Rodolfo, autor. ; Llibre, Jaume, supervisor acadèmic. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques.
En este trabajo presentamos nuevos resultados en la teoría del promedio para encontrar soluciones periódicas. Usando reducción de Lyapunov-Schmidt y el grado de Brouwer nosotros elaboramos un teorema del promedio capaz de detectar la persistencia de soluciones periódicas en sistemas diferenciales cuando este tiene un continuo de ceros en la primera ecuación promediada no nula. [...]
This work presents new results in the averaging theory for finding periodic solutions. Using Lyapunov-Schmidt reduction and Brouwer's degree we elaborate an averaging theorem able to detect the persistence of periodic solutions in differential systems when the first nonvanishing averaged equation has a continuum of zeros. [...]

[Barcelona] : Universitat Autònoma de Barcelona, 2019.  

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