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Articles, 31 registres trobats
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Articles 31 registres trobats  1 - 10següentfinal  anar al registre:
1.
9 p, 569.4 KB Bifurcation of limit cycles from a two-dimensional center inside Rn / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Amar (University of Annaba. Department of Mathematics (Algeria))
We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in Rn perturbed inside a class of piecewise linear differential systems, which appears in a natural way in control theory. [...]
2010 - 10.1016/j.na.2009.08.022
Nonlinear Analysis : Theory, Methods and Applications, Vol. 72, Issue 3-4 (February 2010) , p. 1387-1392  
2.
Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil)) ; Zeli, Iris O. (Instituto Tecnológico de Aeronáutica. Departamento de Matemática (Brazil))
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed non-autonomous n-dimensional discontinuous piecewise smooth differential system. [...]
2020 - 10.4171/rmi/1131
Revista Matemática Iberoamericana, Vol. 36, Núm. 1 (2020) , p. 291-318  
3.
18 p, 893.2 KB Periodic solutions for a class of Duffing differential equations / Feddaoui, Amina (University of Annaba. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics (Algeria))
We provide sufficient conditions for the existence of periodic solutions in the class of Duffing differential equations x" + c(t)x' + a(t)x + b(t)x3 = h(t,x), where the functions a(t), b(t), c(t) and h(t,x) are C2 and T-periodic in the variable t.
2019 - 10.2478/mjpaa-2019-0007
Moroccan Journal of Pure and Applied Analysis, Vol. 5, Issue 1 (June 2019) , p. 86-103
2 documents
4.
11 p, 295.2 KB Periodic solutions of a class of Duffing differential equations / Benterki, Rebiha (Université de Bordj Bou Arréridj. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study the existence of new periodic solutions for the well knwon class of Duffing differential equation of the form x" + cx' + a(t)x + b(t)x3 = h(t), where c is a real parameter, a(t), b(t) and h(t) are continuous T-periodic functions. [...]
2019 - 10.12150/jnma.2019.167
Journal of Nonlinear Modeling and Analysis, Vol. 1, Issue 2 (June 2019) , p. 167-177  
5.
16 p, 342.0 KB Periodic solutions of the Duffing differential equation revisited via the averaging theory / Benterki, Rebiha (Université de Bordj Bou Arréridj. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations ¨ y + asiny = bsint and ¨ y + ay−cy3 = bsint, where a, b and c are real parameters.
2019 - 10.12150/jnma.2019.11
Journal of Nonlinear Modeling and Analysis, Vol. 1, Issue 1 (March 2019) , p. 11-26  
6.
17 p, 362.7 KB A new result on averaging theory for a class of discontinuous planar differential systems with applications / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil))
We develop the averaging theory at any order for computing the periodic solutions of periodic discontinuous piecewise differential system of the form dr/dθ= r'={F+(θ, r, ϵ) if 0≤ θ ≤ α, F-(θ, r, ϵ) if α ≤ θ ≤ 2π, where F±(θ, r, ϵ) = Σk i=1 ϵiF± i (θ, r) + ϵk+1R ± (θ, r, ϵ) with θ ϵ S and r ϵ D, where D is an open interval of ℝ+, and ϵ is a small real parameter. [...]
2017 - 10.4171/rmi/970
Revista Matemática Iberoamericana, Vol. 33, Issue 4 (2017) , p. 1247-1265  
7.
The centers and their cyclicity for a class of polynomial differential systems of degree 7 / Benterki, Rebiha (Université Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We classify the global phase portraits in the Poincaré disc of the generalized Kukles systems ẋ=−y,ẏ=x+axy6+bx3y4+cx5y2+dx7,which are symmetric with respect to both axes of coordinates. Moreover using the averaging theory up to sixth order, we study the cyclicity of the center located at the origin of coordinates, i. [...]
2020 - 10.1016/j.cam.2019.112456
Journal of computational and applied mathematics, Vol. 368 (April 2020) , art. 112456  
8.
Bifurcations from families of periodic solutions in piecewise differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil)) ; Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
Consider a differential system of the form x'=F0(t,x)+∑ki=1εiFi(t,x)+εk+1R(t,x,ε),where Fi:S1×D → Rm and R:S1×D×(−ε0,ε0)→ Rm are piecewise Ck+1 functions and T-periodic in the variable t. [...]
2020 - 10.1016/j.physd.2020.132342
Physica, Vol. 404 (March 2020) , art. 132342  
9.
14 p, 238.1 KB Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Lopes, Bruno D. (Universidade Estadual de Campinas (Brasil). Instituto de Matemática, Estatística e Computação Científica) ; De Moraes, Jaime R. (Universidad Estatal de Mato Grosso del Sur (Brasil))
In this paper we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. [...]
2018
Electronic journal of differential equations, Vol. 2018, No. 118 (2018) , p. 1-14  
10.
30 p, 1.1 MB Global dynamics of a SD oscillator / Chen, Hebai (Fuzhou University. College of Mathematics and Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences)
In this paper we derive the global bifurcation diagrams of a SD oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter a. We research all possible bifurcations of this system, including Pitchfork bifurcation, degenerate Hopf bifurcation, Homoclinic bifurcation, Double limit cycle bifurcation, Bautin bifurcation and Bogdanov-Takens bifurcation. [...]
2018 - 10.1007/s11071-017-3979-y
Nonlinear dynamics, Vol. 91, issue 3 (Feb. 2018) , p. 1755-1777  

Articles : 31 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 1 registres trobats  
1.
132 p, 1.2 MB Dois métodos para a investigação de ciclos limites que bifurcam de centros / Rezende, Alex Carlucci ; Oliveira, Regilene Delazari dos Santos, dir.
Um dos mais investigados problemas na teoria qualitativa dos sistemas dinâmicos no plano é o XVI problema de Hilbert que trata dos ciclos limites. Mais precisamente, a segunda parte do referido problema questiona sobre o número máximo de ciclos limites de um sistema diferencial polinomial plano de grau n. [...]
One of the most investigated problems in the qualitative theory of dynamical systems in the plane is the XVI Hilbert's problem which deals with limit cycles. More precisely, the second part of the problem asks about the maximum number of limit cycles of a polynomial differential system of degree n. [...]

2011  

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