1.
|
|
2.
|
|
3.
|
|
4.
|
|
5.
|
10 p, 4.2 MB |
The zero-Hopf bifurcations of a four-dimensional hyperchaotic system
/
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (Zhuhai))
We consider the four-dimensional hyperchaotic system ẋ=a(y-x), y˙=bx+u-y-xz, ż=xy-cz, and u˙=-du-jx+exz, where a, b, c, d, j, and e are real parameters. This system extends the famous Lorenz system to four dimensions and was introduced in Zhou et al. [...]
2021 - 10.1063/5.0023155
Journal of Mathematical Physics, Vol. 62, Issue 5 (May 2021) , art. 052703
2 documents
|
|
6.
|
|
7.
|
13 p, 4.1 MB |
Global dynamics of a Lotka-Volterra system in ℝ³
/
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Martínez, Y. Paulina (Centre de Recerca Matemàtica) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica (Portugal))
In this work we consider the Lotka-Volterra system in R³ x˙ = −x(x − y − z), y˙ = −y(−x + y − z), z˙ = −z(−x − y + z), introduced recently in [7], and studied also in [8] and [14]. [...]
2020 - 10.1080/14029251.2020.1757240
Journal of Nonlinear Mathematical Physics, Vol. 27, Issue 3 (May 2020) , p. 509-519
|
|
8.
|
12 p, 926.4 KB |
On the periodic orbits of Hamiltonian systems
/
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Rodrigues, Ana (Universidade do Porto. Centro de Matemática (Portugal))
We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the periodic orbits of these integrable systems, first perturbing the Hooke Hamiltonian with a nonautonomous potential, and second perturbing the Kepler problem with an autonomous potential.
2010 - 10.1063/1.3387343
Journal of Mathematical Physics, Vol. 51, Issue 4 (April 2010) , art. 042704
|
|
9.
|
|
10.
|
|