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RESEARCH PAPERS

Nonlinear Response and Suppression of Chaos by Weak Harmonic Perturbation Inside a Triple Well Φ6-Rayleigh Oscillator Combined to Parametric Excitations

[+] Author and Article Information
M. Siewe Siewe

Laboratoire de Mécanique, Départment de Physique, Faculté des Sciences, Université de Yaoundé I, B.P. 812, Yaounde, Camerounctchawoua@uycdc.uninet.cm

F. M. Moukam Kakmeni

Laboratory of Researches on Advanced Materials and Nonlinear Sciences, Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, Camerounfmoukam@uycdc.uninet.cm

C. Tchawoua

Laboratoire de Mécanique, Départment de Physique, Faculté des Sciences, Université de Yaoundé I, B.P. 812, Yaounde, Camerounmsiewe@uycdc.uninet.cm

P. Woafo

Laboratory of Nonlinear Modelling and Simulation in Engineering and Biological Physics, Département de Physique, Faculté des Sciences, Université de Yaoundé I, B.P. 812, Yaoundé, Camerounpwoafo@uycdc.uninet.cm

1

Corresponding author; Permanent address: B.P. 8329, Yaoundé, Cameroun

J. Comput. Nonlinear Dynam 1(3), 196-204 (Feb 15, 2006) (9 pages) doi:10.1115/1.2198215 History: Received July 23, 2005; Revised February 15, 2006

The nonlinear response and suppression of chaos by weak harmonic perturbation inside a triple well Φ6-Rayleigh oscillator combined to parametric excitations is studied in this paper. The main attention is focused on the dynamical properties of local bifurcations as well as global bifurcations including homoclinic and heteroclinic bifurcations. The original oscillator is transformed to averaged equations using the method of harmonic balance to obtain periodic solutions. The response curves show the saddle-node bifurcation and the multi-stability phenomena. Based on the Melnikov’s method, horseshoe chaos is found and its control is made by introducing an external periodic perturbation.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 6

(a) Chaotic oscillations for F0=0.05; (b) regularized oscillation F0=0.028; μ=0.11, ω=0.5, c1=0.012, and c2=0.012

Grahic Jump Location
Figure 5

(a) Chaotic oscillations for F0=0.12; (b) regularized oscillation F0=0.32; ω=0.5, μ=0.11, c1=0.012, and c2=0.011

Grahic Jump Location
Figure 4

(a) Evolution of functions F0R3(ω),μHhet2(ω), and Hhet of Eq. 31 for μ=0.11,c2=0.011, and F0=0.15. (b) Evolution of functions −F0K3(ω),−μHhom2(ω), and Hhom of Eq. 31 for μ=0.11, c2=0.012, and F0=0.15.

Grahic Jump Location
Figure 3

(a) Heteroclinic bifurcation curves in the (μhe,ω) plane for three values of c2: solid line c2=0.011, dashed line c2=0.01 and dotted line c2=0.008, and (b) homoclinic bifurcation curves in the (μho,ω) plane for three values of c2: solid line c2=0.012, dashed line c2=0.01, and dotted line c2=0.008

Grahic Jump Location
Figure 2

Stable and unstable domains in the parameter space for ρ=0.75: (a) the linear case α=β=0, and (b) the nonlinear case α=−0.6, β=0.086

Grahic Jump Location
Figure 1

(a) Amplitude response curves ρ versus the parametric amplitude μ, (b) frequency-response curves. The other parameters are chosen as: α=−0.6, β=0.086, c1=0.25, and c2=0.108.

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