ANALYSIS OF STOCHASTIC CYCLES IN THE CHEN SYSTEM

被引：30

作者：

Bashkirtseva, Irina ^{[1
]}

Chen, Guanrong ^{[2
]}

Ryashko, Lev ^{[1
]}

机构：

[1] Ural State Univ, Dept Math, Ekaterinburg, Russia

[2] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Hong Kong, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 05期

关键词：

Chen system; cycle; stochastic sensitivity; stochastic system; LORENZ CANONICAL FORM; SENSITIVITY; STABILITY; CHAOS;

D O I：

10.1142/S0218127410026587

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the stochastically forced Chen system in its parameter zone under the transition to chaos via period-doubling bifurcations. We suggest a stochastic sensitivity function technique for the analysis of stochastic cycles. We show that this approach allows to construct the dispersion ellipses of random trajectories for any Poincare sections, and these ellipses reflect the essential features of a spatial arrangement of random trajectories near deterministic cycles. For the Chen system, we demonstrate a growth of stochastic sensitivity of the forced cycles under transition to chaos.

引用

页码：1439 / 1450

页数：12

共 20 条

[1] [Anonymous], LECT NOTES PHYS
[2] [Anonymous], 1984, Random Perturbations of Dynamical Systems
[3] Arnold L, 1998, Random dynamical systems
[4] Sensitivity and chaos control for the forced nonlinear oscillations
Bashkirtseva, I
Ryashko, L
[J]. CHAOS SOLITONS & FRACTALS, 2005, 26 (05) : 1437 - 1451
[5] Stochastic sensitivity of 3D-cycles
Bashkirtseva, IA
Ryashko, LB
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2004, 66 (01) : 55 - 67
[6] On a generalized Lorenz canonical form of chaotic systems
Celikovsky, S
Chen, GR
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (08): : 1789 - 1812
[7] Yet another chaotic attractor
Chen, GR
Ueta, T
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (07): : 1465 - 1466
[8] Dembo M., 1995, Large Deviations Techniques and Applications
[9] Horsthemke W., 1984, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology
[10] Ibrahim R.A., 1985, Parametric Random Vibration

← 1 2 →