Research Article

On The Synchronization of Van Der Pol-Duffing Oscillator

Volume: 40 Number: 2 June 30, 2019
Selahattin Kındıkoğlu , Rıfat Yazıcı
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On The Synchronization of Van Der Pol-Duffing Oscillator

Abstract

The most well known property of chaotic systems is their sensitivity to initial conditions. In this work the criterion presented in literature for synchronizing two chaotic systems is applied to a system consisting of two Van der Pol-Duffing oscillators. First, the route to chaos is investigated for the Duffing oscillator. Furthermore, the Lyapunov function approach is used to design a high dimensional chaotic system. Then certain subsystems of a nonlinear chaotic system are synchronized by linking them with a common signal. Synchronization has been observed when there exists an asymptotic stability and an appropriate Lyapunov function, also by computing all the Lyapunov exponents and Kolmogorov entropy.


Keywords

Chaotic systems,Lypunov exponent

References

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  4. Referans4 T. L. Carroll, L. M. Pecora, Synchronizing Nonautonomous Chaotic Circuits, IEEE Trans. On Circuits and Systems-II, Vol. 40, No. 10, pp. 646-650,1993.
  5. Referans5 T. L. Carroll, L. M. Pecora, Using Chaos to keep Period-Multiplied Systems in Phase, Physical Review E, Vol. 48, No. 4, pp. 2426-2436, 1993.
  6. Referans6 J. K. John, R. E. Amritkar, Synchronization of Unstable Orbits Using Adaptive Control, Physical Review E, vol. 49, No. 6, pp. 4843-4847, 1994.
  7. Referans7 K. Murali, M. Lakshmanan, Transmission of Signals by Synchronization in a Chaotic Van der Pol-Duffing Oscillator, Physical Review E, Vol.48, No.3, pp. R1624-R1626, 1993.
  8. Referans8 G. P. King, S. T. Gaito, Bistable Chaos I Unfolding the Cusp, Physical Review A, Vol. 46, No.6, pp. 3092- 3099, 1992.
  9. Referans9 V. English, W. Lauterborn, Regular Window Sructure of a Double-Well Duffing Oscillator, Physical Review A, Vol. 44, No. 2, pp. 916-924, 1991.
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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Publication Date

June 30, 2019

Submission Date

July 18, 2018

Acceptance Date

April 21, 2019

Published in Issue

Year 2019 Volume: 40 Number: 2

DOI

https://doi.org/10.17776/csj.445260

IZ

https://izlik.org/JA76SY23DK

Cite

RIS / Bibtex
APA
Kındıkoğlu, S., & Yazıcı, R. (2019). On The Synchronization of Van Der Pol-Duffing Oscillator. Cumhuriyet Science Journal, 40(2), 340-346. https://doi.org/10.17776/csj.445260
AMA
1.Kındıkoğlu S, Yazıcı R. On The Synchronization of Van Der Pol-Duffing Oscillator. CSJ. 2019;40(2):340-346. doi:10.17776/csj.445260
Chicago
Kındıkoğlu, Selahattin, and Rıfat Yazıcı. 2019. “On The Synchronization of Van Der Pol-Duffing Oscillator”. Cumhuriyet Science Journal 40 (2): 340-46. https://doi.org/10.17776/csj.445260.
EndNote
Kındıkoğlu S, Yazıcı R (June 1, 2019) On The Synchronization of Van Der Pol-Duffing Oscillator. Cumhuriyet Science Journal 40 2 340–346.
IEEE
[1]S. Kındıkoğlu and R. Yazıcı, “On The Synchronization of Van Der Pol-Duffing Oscillator”, CSJ, vol. 40, no. 2, pp. 340–346, June 2019, doi: 10.17776/csj.445260.
ISNAD
Kındıkoğlu, Selahattin - Yazıcı, Rıfat. “On The Synchronization of Van Der Pol-Duffing Oscillator”. Cumhuriyet Science Journal 40/2 (June 1, 2019): 340-346. https://doi.org/10.17776/csj.445260.
JAMA
1.Kındıkoğlu S, Yazıcı R. On The Synchronization of Van Der Pol-Duffing Oscillator. CSJ. 2019;40:340–346.
MLA
Kındıkoğlu, Selahattin, and Rıfat Yazıcı. “On The Synchronization of Van Der Pol-Duffing Oscillator”. Cumhuriyet Science Journal, vol. 40, no. 2, June 2019, pp. 340-6, doi:10.17776/csj.445260.
Vancouver
1.Selahattin Kındıkoğlu, Rıfat Yazıcı. On The Synchronization of Van Der Pol-Duffing Oscillator. CSJ. 2019 Jun. 1;40(2):340-6. doi:10.17776/csj.445260

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