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Articles, 150 registres trobats
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Articles 150 registres trobats  1 - 10següentfinal  anar al registre:
1.
On the periodic orbits of the continuous-discontinuous piecewise differential systems with three pieces separated by two parallel straight lines / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)
During these last twenty years many papers have been published about the piecewise differential systems in the plane. The increasing interest on these kind of differential systems mainly is due to their big number of applications for modeling many natural phenomena. [...]
2023 - 10.1016/j.cnsns.2023.107421
Communications in nonlinear science and numerical simulation, Vol. 125 (October 2023) , art. 107421  
2.
The limit cycles of a class of piecewise differential systems / Benabdallah, Imane (University Mohamed El Bachir. Department of Mathematics) ; Benterki, Rebiha (University Mohamed El Bachir. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this century many papers have been published on the piecewise differential systems in the plane. The increasing interest for this class of differential systems is motivated by their many applications for modelling several natural phenomena. [...]
2023 - 10.1007/s40590-023-00535-x
Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 3 (November 2023) , art. 62  
3.
Limit cycles of a continuous piecewise differential system formed by a quadratic center and two linear centers / Anacleto, Maria Elisa (Universidad del Bío-Bío. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
The study of limit cycles of planar differential systems is one of the main and difficult problems for understanding their dynamics. Thus the objective of this paper is to study the limit cycles of continuous piecewise differential systems in the plane separated by a non-regular line Σ. [...]
2023 - 10.1007/s40590-023-00501-7
Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 2 (July 2023) , art. 29  
4.
10 p, 2.1 MB Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness / Juher, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística) ; Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística) ; Saldaña, Joan (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend on the disease prevalence in a non-linear way. [...]
2023 - 10.1016/j.physd.2023.133714
Physica D. Nonlinear phenomena, Vol. 448 (June 2023) , art. 133714  
5.
17 p, 375.4 KB Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres / Buzzi, Claudio (Universidade Estadual Paulista Julio de Mesquita Filho. Departamento de Matemática) ; Carvalho, Yagor Romano (Universidade de São Paulo. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. [...]
2022 - 10.1080/14689367.2022.2122779
Dynamical Systems, Vol. 37, Issue 4 (2022) , p. 710-728  
6.
11 p, 634.0 KB Non-existence and uniqueness of limit cycles in a class of generalized Liénard equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We provide a sharp upper bound for the number of limit cycles of the generalized Liénard differential systems x˙ = y + axn + bxk, y˙ = cxm where n, k, m are positive integers, 1 < n< k and a, b, c∈ R with bc≠ 0. [...]
2022 - 10.1007/s40590-022-00433-8
Boletin de la Sociedad Matematica Mexicana, Vol. 28, Issue 2 (July 2022) , art. 41  
7.
12 p, 669.3 KB On the Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Formed by Two Rigid Centers Governed by Odd Degree Polynomials / Carvalho, Tiago (Universidade de São Paulo. Departamento de Computação e Matemática) ; Gonçalves, Luiz Fernando (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide an upper bound for the maximum number of limit cycles for the class of discontinuous piecewise differential systems formed by two differential systems separated by the straight line x = 0, one of which is a linear rigid center while the other is a rigid center formed of a linear part plus a homogeneous polynomial of odd degree. [...]
2022 - 10.1142/S0218127422502455
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 16 (December 2022) , art. 2250245  
8.
23 p, 413.2 KB Limit cycles of a class of discontinuous piecewise differential systems separated by the curve y = xn via averaging theory / Guo, Zhifei (Sichuan University. School of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently there is increasing interest in studying the limit cycles of the piecewise differential systems due to their many applications. In this paper we prove that the linear system ẋ = y, ẏ = -x, can produce at most seven crossing limit cycles for n ≥ 4 using the averaging theory of first order, where the bounds ≤ 4 for n ≥ 4 even and the bounds ≤ 7 for n ≥ 5 odd are reachable, when it is perturbed by discontinuous piecewise polynomials formed by two pieces separated by the curve y = xn (n ≥ 4), and having in each piece a quadratic polynomial differential system. [...]
The study of the limit cycles of planar differential systems is one of the main problems in the qualitative theory of differential systems. These last years a big interest appeared for studying the limit cycles of the piecewise differential systems due to their many applications. [...]

2022 - 10.1142/S0218127422501875
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 12 (September 2022) , art. 2250187  
9.
14 p, 333.2 KB Limit cycles of the discontinuous piecewise differential systems on the cylinder / Li, Jie (Sichuan University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In order to understand the dynamics of the differential systems the limit cycles play a main role, but in general their study is not easy. These last years an increasing interest appeared for studying the limit cycles of some classes of discontinuous piecewise differential systems, due to the rich applications of this kind of differential systems. [...]
2022 - 10.11948/20220031
Journal of Applied Analysis and Computation, Vol. 12, Issue 3 (June 2022) , p. 952-963
2 documents
10.
45 p, 594.9 KB Limit Cycles of piecewise-continuous differential systems formed by linear and quadratic isochronous centers II / Ghermoul, Bilal (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))
We study the crossing periodic orbits and limit cycles of the planar piecewise-continuous differential systems separated by the straight-line x = 0 having in x > 0 the general quadratic isochronous center ẋ = -y + x2, y˙ = x(1 + y) after an affine transformation, and in x < 0 an arbitrary quadratic isochronous center except for the quadratic isochronous center ẋ = -y + x2 - y2, y˙ = x(1 + 2y) which has been studied in [Ghermoul et al. [...]
2022 - 10.1142/S0218127422500912
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 6 (May 2022) , art. 2250091  

Articles : 150 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 1 registres trobats  
1.
199 p, 1.4 MB Limit cycles and critical periods for some polynomial differential equations / Sanchez Sanchez, Ivan ; Torregrosa, Joan, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
La present tesi doctoral s'emmarca en l'estudi dels problemes de centre i ciclicitat, així com d'isocronia i criticalitat, en el context de la teoria qualitativa d'equacions diferencials. Aquesta memòria està organitzada en tres capítols. [...]
La presente tesis doctoral se enmarca en el estudio de los problemas de centro y ciclicidad, así como de isocronía y criticalidad, en el contexto de la teoría cualitativa de ecuaciones diferenciales. [...]
The present doctoral thesis is framed in the study of the center and cyclicity problems, as well as isochronicity and criticality, in the context of the qualitative theory of differential equations. This memory is organized in three chapters. [...]

2021  

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