Research Article
Year 2019,
Volume: 40 Issue: 2, 340 - 346, 30.06.2019
Abstract
References
- Referans1 R. He, P. G. Vaidya , Analysis and Synthesisof synchronous Periodic and Chaotic Systems, Physical Review A, Vol. 46, No. 12, pp.7387-7392, 1992.
- Referans2 L. M. Pecora , T. L. Carroll, Synchronization in Chaotic Systems, Physical Review Letters, Vol. 64, No. 8, pp.821-824, 1990.
- Referans3 K. M. Cuomo, A.W. Oppenheim, S. H. Strogatz, Synchronization of Lorenz-Based Chaotic Circuits with Applications to communication, IEEE Trans. On Circuit and Systems-II, Vol. 40, No. 10, pp.626-633, 1993.
- 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.
- 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.
- 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.
- 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.
- Referans8 G. P. King, S. T. Gaito, Bistable Chaos I Unfolding the Cusp, Physical Review A, Vol. 46, No.6, pp. 3092- 3099, 1992.
- 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.
- Referans10 Shinners, S. M., Modern Control System Theory and Desing, John Wiley and Sons, Inc., 1992.
- Referans11 Hilborn, R. C., Chaos and Nonlinear Dynamics, An Introduction for Scientists and Engineers, New York, Oxford , Oxford University Press, 1994.
- Referans12 U. E. Vincent, B. R. Nana Nbendjo, A. A. Ajayi, A. N. Njah, P. V. E. McClintock, Hyperchaos and bifurcations in a driven Van der Pol-Duffing Oscillator circuit, Int. J. Dynam. Control (2015) 3:363-370.
- Referans13 S. Kındıkoğlu, R. Yazıcı, A. I. Kopya, hyperchaos in Van der Pol-Duffing Oscillaor, 19.04. 2000, Turkish Pyhsical Society.
Year 2019,
Volume: 40 Issue: 2, 340 - 346, 30.06.2019
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
References
- Referans1 R. He, P. G. Vaidya , Analysis and Synthesisof synchronous Periodic and Chaotic Systems, Physical Review A, Vol. 46, No. 12, pp.7387-7392, 1992.
- Referans2 L. M. Pecora , T. L. Carroll, Synchronization in Chaotic Systems, Physical Review Letters, Vol. 64, No. 8, pp.821-824, 1990.
- Referans3 K. M. Cuomo, A.W. Oppenheim, S. H. Strogatz, Synchronization of Lorenz-Based Chaotic Circuits with Applications to communication, IEEE Trans. On Circuit and Systems-II, Vol. 40, No. 10, pp.626-633, 1993.
- 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.
- 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.
- 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.
- 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.
- Referans8 G. P. King, S. T. Gaito, Bistable Chaos I Unfolding the Cusp, Physical Review A, Vol. 46, No.6, pp. 3092- 3099, 1992.
- 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.
- Referans10 Shinners, S. M., Modern Control System Theory and Desing, John Wiley and Sons, Inc., 1992.
- Referans11 Hilborn, R. C., Chaos and Nonlinear Dynamics, An Introduction for Scientists and Engineers, New York, Oxford , Oxford University Press, 1994.
- Referans12 U. E. Vincent, B. R. Nana Nbendjo, A. A. Ajayi, A. N. Njah, P. V. E. McClintock, Hyperchaos and bifurcations in a driven Van der Pol-Duffing Oscillator circuit, Int. J. Dynam. Control (2015) 3:363-370.
- Referans13 S. Kındıkoğlu, R. Yazıcı, A. I. Kopya, hyperchaos in Van der Pol-Duffing Oscillaor, 19.04. 2000, Turkish Pyhsical Society.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2019 |
| Submission Date | July 18, 2018 |
| Acceptance Date | April 21, 2019 |
| Published in Issue | Year 2019Volume: 40 Issue: 2 |