Chaotic Dynamics in Duffing System with Two External Forcings

Shu Guang Zhang; Zhi Yong Zhu; Zhi Guo

doi:10.4028/www.scientific.net/AMR.216.777

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 216Chaotic Dynamics in Duffing System with Two...

Chaotic Dynamics in Duffing System with Two External Forcings

Abstract:

Duffing system with two external forcing terms is investigated in detail. The criterion of existence of chaos under the periodic perturbation is given by using Melnikov's method. Numerical simulations including heteroclinic and homoclinic bifurcation surfaces, bifurcation diagrams, maximum lyapunov exponents and Poincare map are given to illustrate the theoretical analysis.

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Periodical:

Advanced Materials Research (Volume 216)

Pages:

777-781

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.216.777

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Online since:

March 2011

Authors:

Shu Guang Zhang, Zhi Yong Zhu, Zhi Guo

Keywords:

Chaos, Duffing System, Melnikov Method

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References

[1] Chacon R, Bejarano JD. Homoclinic and heteroclinic chaos in a triple-well oscillator. Journal of Sound and Vibration 1995; 186(2): 269-278.

DOI: 10.1006/jsvi.1995.0448

Google Scholar

[2] Guckenheimer J, Homel P. Nonlinear oscillations, Dynamical System, and Bifurcation of Vector Fields. Springer-Verlag, (1992).

Google Scholar

[3] Holmes P, Whitley D. On the attacting set for Duffing's equation. Physicia D. 1983: 111-123.

Google Scholar

[4] Jing ZJ, Wang RQ. Complex dynamics in Duffing system with two external forcings. Chaos, Solitons and Fractals 2005; 23: 399-411.

DOI: 10.1016/j.chaos.2004.02.022

Google Scholar

[5] Li GX, Moon FC. Criteria for chaos of a three-well potential oscillator with homoclinic and heteroclinic orbits. Journal of Sound and Vibration 1990; 136(1): 17-34.

DOI: 10.1016/0022-460x(90)90934-r

Google Scholar

[6] Li W, Xu W, Zhao JF, Ma SJ. Stochastic optimal control of first-passage failure for coupled Duffing-Van der pol system under Gaussian white noise excitations. Chaos, Solitons and Fractals 2005; 25: 1221-1228.

DOI: 10.1016/j.chaos.2004.11.066

Google Scholar

[7] Parlitz V, Lauterborn W. Supersturcture in the bifurcation set of the Duffing equation. Physics Letters A 1985; 107: 351-355.

DOI: 10.1016/0375-9601(85)90687-5

Google Scholar

[8] Rajasekar S, Murali K. Resonance behaviors and jump phenomena in a two coupled Duffing-Van der pol oscillators. Chaos, Solitons and Fractals 2004; 19: 925-934.

DOI: 10.1016/s0960-0779(03)00277-7

Google Scholar

[9] Souza SLTde, Caldas IL, Viana RL, Baathazar JM, Brasil RMLRF. Basins of attraction changes by amplitude constraining of oscillators with limited power supply. Chaos, Solitons and Fractals 2005; 26: 1211-1220.

DOI: 10.1016/j.chaos.2005.02.039

Google Scholar

[10] Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. New York, Springer-Verlag, (1990).

Google Scholar