Results overview: Found 30 records in 0.02 seconds.
Articles, 27 records found
Research literature, 3 records found
Articles 27 records found  1 - 10nextend  jump to record:
1.
10 p, 652.9 KB Limit cycles for a class of third-order differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiaotong University. Department of Mathematics (China)) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics (China))
In this paper we study the limit cycles of the third-order differential equation . . . x − μẍ + ẋ − μx = εF(x, ẋ , ẍ, t) where μ ≠ 0, ε is small enough and F Є C2 is a 2π-periodic function of variable t.
2010 - 10.1216/RMJ-2010-40-2-581
The Rocky Mountain Journal of Mathematics, Vol. 40, Issue 2 (2010) , p. 581-594
2 documents
2.
8 p, 714.8 KB Rational first integrals in the Darboux theory of integrability in Cn / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics (China))
In 1976 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in Rn or Cn of degree d is at least (d + n/n− 1) + n, then the vector field has a rational first integral. [...]
2010 - 10.1016/j.bulsci.2007.12.001
Bulletin des Sciences Mathematiques, Vol. 134, Issue 2 (March 2010) , p. 189-195  
3.
12 p, 271.2 KB On the integrability of the Hamiltonian systems with homogeneus polynomial potentials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
We summarize the known results on the integrability of the complex Hamiltonian systems with two degrees of freedom defined by the Hamiltonian functions of the form H = 1/2 2 ∑ i=1 p2i + V (q1,q2), where V (q1,q2) are homogeneous polynomial potentials of degree k.
2018 - 10.2478/AMNS.2018.2.00041
Applied Mathematics and Nonlinear Sciences, Vol. 3, Issue 2 (July 2018) , p. 527-536
2 documents
4.
15 p, 300.7 KB Piecewise linear differential systems with an algebraic line of separation / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Key Laboratory of Scientific and Engineering Computing (China))
We study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each n ∈ N there exist piecewise linear differential systems separated by an algebraic curve of degree n having [n/2] hyperbolic limit cycles. [...]
2020
Electronic journal of differential equations, Vol. 2020, Issue 19 (2020) , p. 1-14
2 documents
5.
21 p, 336.3 KB Limit cycles created by piecewise linear centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences)
In the last few years, the interest for studying the piecewise linear differential systems has increased strongly, mainly due to their applications to many physical phenomena. In the study of these differential systems, the limit cycles play a main role. [...]
2019 - 10.1063/1.5086018
Chaos, Vol. 29, Issue 5 (May 2019) , art. 053116  
6.
The period function of Hamiltonian systems with separable variables / Villadelprat, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
In this paper we study the period function of those planar Hamiltonian differential systems for which the Hamiltonian function H(x, y) has separable variables, i. e. , it can be written as H(x, y) = F1(x) + F2(y). [...]
2020 - 10.1007/s10884-019-09759-w
Journal of dynamics and differential equations, Vol. 32, Issue 2 (June 2020) , p. 741-767  
7.
17 p, 402.2 KB Limit cycles of the classical Liénard differential systems : A survey on the Lins Neto, de Melo and Pugh's conjecture / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences)
In 1977 Lins Neto et al. (1977) conjectured that the classical Liénard system ẋ=y−F(x),ẏ=−x with F(x) a real polynomial of degree n, has at most [(n−1)/2] limit cycles, where [⋅] denotes the integer part function. [...]
2017 - 10.1016/j.exmath.2016.12.001
Expositiones Mathematicae, Vol. 35, Issue 3 (September 2017) , p. 286-299  
8.
13 p, 380.0 KB Dynamics of some three-dimensional Lotka-Volterra systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences)
We characterize the dynamics of the following two Lotka-Volterra differential systems: ̇x=x(r+ay+bz), ̇x=x(r+ax+by+cz), ̇y=y(r−ax+cz),and ̇y=y(r+ax+dy+ez), ̇z=z(r−bx−cy), ̇z=z(r+ax+dy+fz). [...]
2017 - 10.1007/s00009-017-0927-5
Mediterranean Journal of Mathematics, Vol. 14, Issue 3 (June 2017) , art. 126  
9.
19 p, 430.8 KB Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
We study how to change the maximum number of limit cycles of the discontinuous piecewise linear differential systems with only two pieces in function of the degree of the discontinuity of the algebraic curve between the two linear differential systems. [...]
2019 - 10.1142/S0218127419500172
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 29, Núm. 2 (February 2019) , art. 1950017  
10.
17 p, 373.5 KB The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
We provide sufficient conditions for the non-existence, existence and uniqueness of limit cycles surrounding a focus of a quadratic polynomial differential system in the plane.
2019 - 10.1017/S0308210517000221
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 149, Issue 1 (February 2019) , p. 1-14  

Articles : 27 records found   1 - 10nextend  jump to record:
Research literature 3 records found  
1.
10 p, 187.9 KB Rational first integrals in the Darboux theory of integrability in Cn / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"Vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2008 (Prepublicacions del Centre de Recerca Matemàtica ; 789)  
2.
21 p, 263.3 KB Hopf bifurcation in higher dimensional differential systems via the averaging method / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2008 (Prepublicacions del Centre de Recerca Matemàtica ; 788)  
3.
18 p, 239.1 KB Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds / Liu, Fei (Shanghai Jiaotong University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"Vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2008 (Prepublicacions del Centre de Recerca Matemàtica ; 787)  

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