Resonances of periodic orbits in the Lorenz system

被引：6

作者：

Algaba, Antonio ^{[1
]}

Gamero, Estanislao ^{[2
]}

Merino, Manuel ^{[1
]}

Rodriguez-Luis, Alejandro J. ^{[2
]}

机构：

[1] Univ Huelva, Dept Matemat, Ctr Invest Fis Teor & Matemat FIMAT, Huelva 21071, Spain

[2] Univ Seville, Dept Matemat Aplicada 2, ES Ingenieros, Camino Descubrimientos S-N, Seville 41092, Spain

来源：

NONLINEAR DYNAMICS | 2016年 / 84卷 / 04期

关键词：

Lorenz equations; Torus bifurcation; Resonance; Arnold's tongue; Global bifurcation; TAKENS-BOGDANOV BIFURCATIONS; HOPF-BIFURCATION; HETEROCLINIC ORBITS; ARNOLDS TONGUES; CHEN; MANIFOLDS; EXISTENCE; FAMILY; CHAOS;

D O I：

10.1007/s11071-016-2632-5

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

Usually, the physical interest of the Lorenz system is restricted to the region where its three parameters are positive. However, this famous system appears, when , in the study of a thermosolutal convection model and in the analysis of traveling-wave solutions of the Maxwell-Bloch equations. In this context, a Takens-Bogdanov bifurcation of heteroclinic type becomes an important organizing center. It has been very recently shown that the periodic orbit born in the Hopf bifurcation of the origin undergoes a torus bifurcation. In this paper we perform a detailed numerical study of the resonances of periodic orbits in the three-parameter Lorenz system, when and . The combination of numerical continuation methods and Poincar, sections of the flow provides important information of how the resonances appear and evolve giving rise to a very rich dynamical and bifurcation scenario.

引用

页码：2111 / 2136

页数：26

共 41 条

[1] A degenerate Hopf-saddle-node bifurcation analysis in a family of electronic circuits
Algaba, A.
Gamero, E.
Garcia, C.
Merino, M.
[J]. NONLINEAR DYNAMICS, 2007, 48 (1-2) : 55 - 76
[2] Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator
Algaba, A
Freire, E
Gamero, E
Rodriguez-Luis, AJ
[J]. NONLINEAR DYNAMICS, 1998, 16 (04) : 369 - 404
[3] Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system
Algaba, A.
Dominguez-Moreno, M. C.
Merino, M.
Rodriguez-Luis, A. J.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 30 (1-3) : 328 - 343
[4] Analysis of the T-point-Hopf bifurcation in the Lorenz system
Algaba, A.
Fernandez-Sanchez, F.
Merino, M.
Rodriguez-Luis, A. J.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 22 (1-3) : 676 - 691
[5] Takens-Bogdanov bifurcations of periodic orbits and Arnold's tongues in a three-dimensional electronic model
Algaba, A
Merino, M
Rodríguez-Luis, AJ
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2001, 11 (02): : 513 - 531
[6] Algaba A, 1999, IEICE T FUND ELECTR, VE82A, P1714
[7] Algaba A., 2008, CHAOS, V18
[8] Resonances of periodic orbits in Rossler system in presence of a triple-zero bifurcation
Algaba, Antonio
Freire, Emilio
Gamero, Estanislao
Rodriguez-Luis, Alejandro J.
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (06): : 1997 - 2008
[9] Study of the Hopf bifurcation in the Lorenz, Chen and Lu systems
Algaba, Antonio
Dominguez-Moreno, Maria C.
Merino, Manuel
Rodriguez-Luis, Alejandro J.
[J]. NONLINEAR DYNAMICS, 2015, 79 (02) : 885 - 902
[10] Comment on "Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems" [Appl. Math. Comput. 218 (2012) 11859-11870]
Algaba, Antonio
Fernandez-Sanchez, Fernando
Merino, Manuel
Rodriguez-Luis, Alejandro J.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 244 : 49 - 56

← 1 2 3 4 5 →