UAB Digital Repository of Documents 72 records found  1 - 10nextend  jump to record: Search took 0.04 seconds. 
1.
Nilpotent Bicenters in Continuous Piecewise Z2 -Equivariant Cubic Polynomial Hamiltonian Vector Fields : Cusp-Cusp Type / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the global dynamics for a class of continuous piecewise Z2-equivariant cubic Hamiltonian vector fields with nilpotent bicenters at (±1, 0). We consider these polynomial vector fields with a challenging case where the bicenters (±1, 0) come from the combination of two nilpotent cusps separated by y = 0. [...]
2023 - 10.1142/S0218127423501389
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 12 (September 2023) , art. 2350138  
2.
Nonexistence and Uniqueness of Limit Cycles in a Class of Three-Dimensional Piecewise Linear Differential Systems / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Huang, Lihong (Changsha University. College of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
During the last twenty years there has been increasing interest in studying the piecewise differential systems, mainly due to their many applications in natural science and technology. Up to now the most studied differential systems are in dimension two, here we study them in dimension three. [...]
2023 - 10.1142/S021812742350075X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 6 (May 2023) , art. 2350075  
3.
52 p, 2.1 MB Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either y2 = x3, or y2 = x2(x + 1), or y2 = x2(x - 1). We classify the phase portraits of all quadratic polynomial differential systems having the invariant cubic y2 = x2(x + 1). [...]
2023 - 10.1142/S0218127423500037
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 1 (January 2023) , art. 2350003  
4.
14 p, 1.1 MB Planar Kolmogorov systems with infinitely many singular points at infinity / Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. [...]
2022 - 10.1142/S0218127422500651
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 5 (April 2022) , art. 2250065  
5.
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  
6.
16 p, 458.9 KB Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by nonregular curves / Jimenez, Johana (Universidade Federal do Oeste da Bahia (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The problem of determining the existence, maximum number and positions of the limit cycles of the planar discontinuous piecewise linear differential systems is an important problem in the qualitative theory of differential systems. [...]
2022 - 10.1142/S021812742250184X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 12 (September 2022) , art. 2250184  
7.
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  
8.
24 p, 1.3 MB Nilpotent center in a continuous piecewise quadratic polynomial Hamiltonian vector field / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by the straight line x = 0, where these kinds of systems have a nilpotent center at (0, 0), which comes from the combination of two cusps of both Hamiltonian systems. [...]
2022 - 10.1142/S0218127422501164
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 8 (June 2022) , art. 2250116  
9.
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  
10.
11 p, 569.3 KB Rocard's 1941 chaotic relaxation econometric oscillator / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon) ; Jovanovic, Franck (Teluq University. Université d'Orléans. School of Business Administration) ; Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In the beginning of the Second World War, the French physicist, Yves Rocard, published a book entitled Théorie des Oscillateurs (Theory of Oscillators). In Chapter V, he designed a mathematical model consisting of a set of three nonlinear differential equations and allowing to account for economic cycles. [...]
2022 - 10.1142/S0218127422500432
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 3 (March 2022) , art. 2250043  

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