Relative effectiveness of weak periodic excitations in suppressing homoclinic/heteroclinic chaos

被引：15

作者：

Chacón, R ^{[1
]}

机构：

[1] Univ Extremadura, Escuela Ingn Ind, Dept Electron & Ingn Eletromecan, E-06071 Badajoz, Spain

来源：

EUROPEAN PHYSICAL JOURNAL B | 2002年 / 30卷 / 02期

关键词：

D O I：

10.1140/epjb/e2002-00375-6

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

Melnikov-method-based theoretical results are demonstrated concerning the relative effectiveness of any two weak excitations in suppressing homoclinic/heteroclinic chaos of a relevant class of dissipative, low-dimensional and non-autonomous systems for the main resonance between the chaos-inducing and chaos-suppressing excitations. General analytical expressions are derived from the analysis of generic Melnikov functions providing the boundaries of the regions as well as the enclosed area in the amplitude/initial phase plane of the chaos-suppressing excitation where homoclinic/heteroclinic chaos is inhibited. The relevance of the theoretical results on chaotic attractor elimination is confirmed by means of Lyapunov exponent calculations for a two-well Duffing oscillator.

引用

页码：207 / 210

页数：4

共 15 条

[1]

Arnold VI, 1964, SOV MATH DOKL, V5, P581

[2] KOLMOGOROV ENTROPY AND NUMERICAL EXPERIMENTS [J].

BENETTIN, G ;

GALGANI, L ;

STRELCYN, JM .

PHYSICAL REVIEW A, 1976, 14 (06) :2338-2345

[3]

Brindley J., 1991, Chaos, Solitons and Fractals, V1, P323, DOI 10.1016/0960-0779(91)90024-4

[4] SUPPRESSION OF PERIOD-DOUBLING AND NONLINEAR PARAMETRIC EFFECTS IN PERIODICALLY PERTURBED SYSTEMS [J].

BRYANT, P ;

WIESENFELD, K .

PHYSICAL REVIEW A, 1986, 33 (04) :2525-2543

[5] SUPPRESSION OF CHAOS BY SELECTIVE RESONANT PARAMETRIC PERTURBATIONS [J].

CHACON, R .

PHYSICAL REVIEW E, 1995, 51 (01) :761-764

[6] Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations [J].

Chacón, R .

EUROPHYSICS LETTERS, 2001, 54 (02) :148-153

[7] Maintenance and suppression of chaos by weak harmonic perturbations:: A unified view [J].

Chacón, R .

PHYSICAL REVIEW LETTERS, 2001, 86 (09) :1737-1740

[8] General results on chaos suppression for biharmonically driven dissipative systems [J].

Chacón, R .

PHYSICS LETTERS A, 1999, 257 (5-6) :293-300

[9] Comparison between parametric excitation and additional forcing terms as chaos-suppressing perturbations [J].

Chacón, R .

PHYSICS LETTERS A, 1998, 249 (5-6) :431-436

[10] EXPERIMENTAL-EVIDENCE OF SUPPRESSION OF CHAOS BY RESONANT PARAMETRIC PERTURBATIONS [J].

FRONZONI, L ;

GIOCONDO, M ;

PETTINI, M .

PHYSICAL REVIEW A, 1991, 43 (12) :6483-6487

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