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Articles 24 records found  beginprevious15 - 24  jump to record: Search took 0.02 seconds. 
15.
15 p, 517.2 KB Perturbed damped pendulum: finding periodic solutions via averaging method / Novaes, Douglas D. (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
Using the damped pendulum model we introduce the averaging method to study the periodic solutions of dynamical systems with small non-autonomous perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non-linear perturbed damped pendulum. [...]
2013 - 10.1590/s1806-11172013000100014
Revista Brasileira de Ensino de Física, Vol. 35 Núm. 1 (2013) , p. 7 pages  
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16.
15 p, 433.8 KB On the birth of limit cycles for non-smooth dynamical systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brazil). Departamento de Matemática) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas (Brazil). Departamento de Matemática)
The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. [...]
2015 - 10.1016/j.bulsci.2014.08.011
Bulletin des Sciences Mathematiques, Vol. 139 (2015) , p. 229-244  
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17.
21 p, 834.8 KB Averaging theory for discontinuous piecewise differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (Universidade Federal de Sao Carlos (Brazil). Departamento de Física, Química e Matematica) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brazil). Departamento de Matematica)
We develop the averaging theory of first and second order for studying the periodic solutions of discontinuous piecewise differential systems in arbitrary dimension and with an arbitrary number of systems with the minimal conditions of differentiability. [...]
2015 - 10.1016/j.jde.2015.01.022
Journal of differential equations, Vol. 258 (2015) , p. 4007-4032  
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18.
20 p, 413.0 KB Stability of singular limit cycles for Abel equations / Bravo, Jose Luis (Universidad de Extremadura. Departamento de Matemáticas) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Fernández, Manuel (Universidad de Extremadura. Departamento de Matemáticas)
We obtain a criterion for determining the stability of singular limit cycles of Abel equations x = A(t)x3 + B(t)x2 . This stability controls the possible saddle-node bifurcations of limit cycles. Therefore, studying the Hopf-like bifurcations at x = 0, together with the bifurcations at infinity of a suitable compactification of the equations, we obtain upper bounds of their number of limit cycles. [...]
2015 - 10.3934/dcds.2015.35.1873
Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 5 (2015) , p. 1873-1890  
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19.
18 p, 581.3 KB Hopf and zero-Hopf bifurcations on the Hindmarsh-Rose system / Buzzi, Claudio (IBILCE-UNESP (Brazil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Medrado, Joao Carlos (IME-UFG (Brazil). Instituto de Matemática e Estatística)
We prove the existence of the classical Hopf bifurcation and of the zero--Hopf bifurcation in the Hindmarsh-Rose system. For doing this some adequate change of parameters must be done in order that the computations become easier.
2015 - 10.1007/s11071-015-2429-y
Nonlinear dynamics, 2015, p. 1-8  
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20.
11 p, 325.5 KB Detecting periodic orbits in some 3d chaotic quadratic polynomial differential systems / de Carvalho, Tiago (Faculdade de Ciências. Departamento de Matemática) ; D. Euzébio, Rodrigo (IMECC-UNICAMP. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; J. Tonon, Durval (Universidade Federal de Goias (Brazil))
Using the averaging theory we study the periodic solutions and their linear stability of the 3-dimensional chaotic quadratic polynomial differential systems without equilibria studied in [3]. All these differential systems depend only on one-parameter.
2015 - 10.3934/dcdsb.2016.21.1
Discrete and continuous dynamical systems. Series B, Vol. 21 Núm. 1 (2015) , p. 1-11  
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21.
7 p, 318.1 KB A Note on Forced Oscillations in Differential Equations with Jumping Nonlinearities / Buica, Adriana (Bolyai University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makarenkov, Oleg (University of Texas at Dallas. Department of Mathematical Sciences)
The goal of this paper is to study bifurcations of asymptotically stable 2-periodic solutions in the forced asymmetric oscillator u c u u a u^ =1 t by means of a Lipschitz generalization of the second Bogolubov's theorem due to the authors. [...]
2015 - 10.1007/s12591-014-0199-5
Differential Equations and Dynamical Systems, Vol. 23 Núm. 4 (2015) , p. 415-421  
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22.
12 p, 390.4 KB Bifurcation of limit cycles from some uniform isochronous centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics)
This article concerns with the weak 16-th Hilbert problem. More precisely, we consider the uniform isochronous centers x'=-y x^(n-1) y, y'= x x^(n-2) y^2 , for n = 2, 3, 4, and we perturb them by all homogeneous polynomial of degree 2, 3, 4, respectively. [...]
2015
Dynamics of Continuous, Discrete and Impulsive Systems. Series A. Mathematical Analysis, Vol. 22, Num. 5 (2015) , p. 381-394  
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23.
42 p, 5.2 MB Invariant tori in the lunar problem / Meyer, Kenneth R. (University of Cincinnati. Department of Mathematical Sciences) ; Palacian, Jesus F. (Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática) ; Yanguas, Patricia (Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática)
Theorems on the existence of invariant KAM tori are established for perturbations of Hamiltonian systems which are circle bundle ows. By averaging the perturbation over the bundle ow one obtains a Hamiltonian system on the orbit (quotient) space by a classical theorem of Reeb. [...]
2014 - 10.5565/PUBLMAT_Extra14_19
Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 353-394  
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24.
23 p, 585.6 KB Delayed logistic population models revisited / Liz, Eduardo (Universidade de Vigo. Departamento de Matemática Aplicada II)
We discuss the global dynamics of some logistic models governed by delay-differential equations. We focus on models of exploited populations, and study the changes in the dynamics as the harvesting effort is increased. [...]
2014 - 10.5565/PUBLMAT_Extra14_17
Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 309-331  
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