DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS

Shko Ali Tahır; Abderrahman B Ouhamıdı; Murat Sarı

DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS

Abstract

In this paper, we propose a generalized method by designing new response systems for solving synchronization problems of coupled chaotic identical and non-identical dynamical systems. We extend our study by considering two new techniques for constructing a chaotic synchronization between two identical or non-identical dynamical systems. The first one is based on the classical Lyapunov stability theory. The proposed method is analyzed by means of equilibrium points, eigenvalue structures, and Lyapunov functions. The second one requires the nonlinear part of the response system to be smooth enough and uses the expansion of such a function. The designed controller functions enable the state variables of the drive system to globally synchronize with the state variables of the response system in both methods. The global convergence of the proposed methods have been discussed by giving two theoretical results. To show the effectiveness and feasibility of those approaches, various numerical simulations have been carried out.

Keywords

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Shko Ali Tahır This is me
0000-0002-6780-7111
Türkiye

Abderrahman B Ouhamıdı This is me
0000-0002-5675-7251
France

Murat Sarı This is me
0000-0003-0508-2917
Türkiye

Publication Date

June 1, 2018

Submission Date

January 16, 2018

Acceptance Date

April 23, 2018

Published in Issue

Year 2018 Volume: 36 Number: 2

IZ

https://izlik.org/JA73PE87LK

Cite

RIS / Bibtex

APA

Tahır, S. A., Ouhamıdı, A. B., & Sarı, M. (2018). DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS. Sigma Journal of Engineering and Natural Sciences, 36(2), 441-457. https://izlik.org/JA73PE87LK

AMA

1.Tahır SA, Ouhamıdı AB, Sarı M. DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS. SIGMA. 2018;36(2):441-457. https://izlik.org/JA73PE87LK

Chicago

Tahır, Shko Ali, Abderrahman B Ouhamıdı, and Murat Sarı. 2018. “DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS”. Sigma Journal of Engineering and Natural Sciences 36 (2): 441-57. https://izlik.org/JA73PE87LK.

EndNote

Tahır SA, Ouhamıdı AB, Sarı M (June 1, 2018) DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS. Sigma Journal of Engineering and Natural Sciences 36 2 441–457.

IEEE

[1]S. A. Tahır, A. B. Ouhamıdı, and M. Sarı, “DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS”, SIGMA, vol. 36, no. 2, pp. 441–457, June 2018, [Online]. Available: https://izlik.org/JA73PE87LK

ISNAD

Tahır, Shko Ali - Ouhamıdı, Abderrahman B - Sarı, Murat. “DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS”. Sigma Journal of Engineering and Natural Sciences 36/2 (June 1, 2018): 441-457. https://izlik.org/JA73PE87LK.

JAMA

1.Tahır SA, Ouhamıdı AB, Sarı M. DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS. SIGMA. 2018;36:441–457.

MLA

Tahır, Shko Ali, et al. “DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS”. Sigma Journal of Engineering and Natural Sciences, vol. 36, no. 2, June 2018, pp. 441-57, https://izlik.org/JA73PE87LK.

Vancouver

1.Shko Ali Tahır, Abderrahman B Ouhamıdı, Murat Sarı. DESIGNING A RESPONSE APPROACH IN CHAOTIC SYSTEMS. SIGMA [Internet]. 2018 Jun. 1;36(2):441-57. Available from: https://izlik.org/JA73PE87LK