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Articles, 19 registres trobats
Articles 19 registres trobats  1 - 10següent  anar al registre:
1.
The Markus-Yamabe conjecture does not hold for discontinuous piecewise linear differential systems separated by one straight line / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Menezes, Lucyjane de A.S. (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil))
The Markus-Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a differentiable system x˙ = f(x) has a singularity and the Jacobian matrix Df(x) has everywhere eigenvalues with negative real part, then the singularity is a global attractor. [...]
2020 - 10.1007/s10884-020-09825-8
Journal of dynamics and differential equations, 2020  
2.
Limit cycles for two classes of control piecewise linear differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ; Rodrigues, Camila A.B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
We study the bifurcation of limit cycles from the periodic orbits of 2n-dimensional linear centers x˙ = A0x when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control theory of the form x˙ = A0x+ ε(Ax+ ϕ(x) b), where ϕ is a continuous or discontinuous piecewise linear function, A0 is a 2n×2n matrix with only purely imaginary eigenvalues, ε is a small parameter, A is an arbitrary 2n×2n matrix, and b is an arbitrary vector of Rn.
2020 - 10.1007/s40863-020-00163-7
São Paulo Journal of Mathematical Sciences, Vol. 14, Issue 1 (June 2020) , p. 49-65  
3.
13 p, 326.6 KB Cyclicity of (1,3)-switching FF type equilibria / Chen, Xingwu (Sichuan University. Department of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University. Department of Mathematics (China))
Hilbert's 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). [...]
2019 - 10.3934/dcdsb.2019153
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 12 (December 2019) , p. 6541-6552  
4.
17 p, 408.6 KB Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences)
We apply the averaging theory of high order for computing the limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. These discontinuous piecewise differential systems are formed by two either quadratic, or cubic polynomial differential systems separated by a straight line. [...]
2019 - 10.3934/dcdsb.2018236
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 4 (April 2019) , p. 1769-1784  
5.
16 p, 360.0 KB On the periodic solutions of the Milchelson continuous and discontinuous piecewise linear differential system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de Sâo Paulo (Brazil). Departamento de Matemática) ; Rodrigues, Camila A. B. (Universidade de São Paulo (Brasil). Departamento de Matemática)
Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michel- son differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system. [...]
2018 - 10.1007/s40314-016-0413-x
Computational & Applied Mathematics, Vol. 37, issue 2 (May 2018) , p. 1550-1561  
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  
7.
16 p, 3.3 MB The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems / Castillo, Juan (Universidad de Sonora (Mèxic). Departamento de Matemáticas) ; Verduzco, Fernando (Universidad de Sonora (Mèxic). Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The creation or destruction of a crossing limit cycle when a sliding segment changes its stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we find an unfolding for such bifurcation, and we prove the existence and uniqueness of a crossing limit cycle for this family.
2017 - 10.1007/s11071-017-3766-9
Nonlinear dynamics, Vol. 90 (2017) , p. 1829-1840  
8.
15 p, 328.5 KB Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems / Chen, Xingwu (Sichuan University (Xina). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)
It is well known that the cyclicity of a Hopf bifurcation in continuous quadratic polynomial differential systems in \R^2 is 3. In contrast here we consider discontinuous differential systems in \R^2 defined in two half--planes separated by a straight line. [...]
2017 - 10.3934/dcdsb.2017203
Discrete and Continuous Dynamical Systems. Series B, Vol. 22 Núm. 10 (2017) , p. 3953-3965  
9.
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)
This work is devoted to study the existence of periodic solutions for a family of planar discontinuous differential systems Z(x,y;) with many zones. We show that for.
2017 - 10.1016/j.physd.2017.05.003
Physica D. Nonlinear phenomena, Vol. 353-354 (2017) , p. 1-10  
10.
13 p, 346.6 KB Piecewise linear differential systems without equilibria produce limit cycles? / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
In this article we study the planar piecewise differential systems formed by two linear differential systems separated by a straight line, such that both linear differential have no equilibria, neither real nor virtual.
2017 - 10.1007/s11071-016-3236-9
Nonlinear dynamics, Vol. 88 (2017) , p. 157-164  

Articles : 19 registres trobats   1 - 10següent  anar al registre:
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