Primary Resonance and Bifurcations in Damped and Driven Duffing-Van der Pol System

Shu Guang Zhang; Zhi Yong Zhu; Zhi Guo

doi:10.4028/www.scientific.net/AMR.216.782

Paper Titles

An Experimental and Analytical Vibration Study of a Thin Cylindrical Shell Treated with Constrained Layer Damping
p.763

Media Access Control Protocols in Multimedia Wireless Sensor Networks: A Survey
p.768

Theoretical Analysis of Young’s Modulus for Unidirectional Fiber Reinforced Composites with Different Fiber Orientations
p.773

Chaotic Dynamics in Duffing System with Two External Forcings
p.777

Primary Resonance and Bifurcations in Damped and Driven Duffing-Van der Pol System
p.782

Radiative Transitions and Optical Behaviors in Tm³⁺ Doped Mixed Alkali/Alkaline-Earth Modified Heavy-Metal Gallate Glasses
p.787

Research on Magnet Excitation and Image Processing Used in Visual Detection
p.793

Process Analysis for Rapid Tooling Technology Based on Rapid Prototyping
p.798

Discussion on Construction of OCDMA PON Address Code-(F,K,2) Optical Orthogonal Codes
p.804

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 216Primary Resonance and Bifurcations in Damped and...

Primary Resonance and Bifurcations in Damped and Driven Duffing-Van der Pol System

Abstract:

In this paper, by using second-order averaging method, damped and driven Duffing-Van der Pol system is investigated in detail. The conditions for the existence and the bifurcations of harmonics are given.

You might also be interested in these eBooks

Optical, Electronic Materials and Applications

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 216)

Pages:

782-786

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.216.782

Citation:

Cite this paper

Online since:

March 2011

Authors:

Shu Guang Zhang, Zhi Yong Zhu, Zhi Guo

Keywords:

Bifurcations, Duffing-Van der Pol System, Second-Order Averaging Methods

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] Guckenheimer, J. and Holmes, P. Dynamical systems and bifurcations of vector fields. New York: Springer-Verlag; (1997).

Google Scholar

[2] Jing, Z.J. and Wang, R.Q. 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

[3] Kapitaniak, T. Analytical condition for chaotic behavior of the Duffing oscillation. Phys Lett A, 1990, 144(6, 7): 322-324.

Google Scholar

[4] Wakako, M., Chieko, M., Koi-ichi, H., Yoshi, H.I. Integrable Duffing's maps and solutions of the Duffing equation. Chaos, Solitons and Fractals, 2003, 15(3): 425-443.

DOI: 10.1016/s0960-0779(02)00089-9

Google Scholar

[5] Yagasaki, K. Homoclinic tangles, phase locking, and chaos in a two frequency perturbation of Duffing's equation. J. Nonlinear Sci, 1999, 9: 131-148.

DOI: 10.1007/s003329900066

Google Scholar

[6] Yagasaki K. Second-order averaging and chaos in quasi-periodically forced weakly nonlinear oscillators. Physica D 1990; 44: 445-458.

DOI: 10.1016/0167-2789(90)90157-k

Google Scholar

[7] Wiggins, S. Introduction to applied nonlinear dynamical systems and chaos. New York: Springer; (1990).

Google Scholar