Applied and Computational Mathematics

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The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method

Received: 13 October 2013    Accepted:     Published: 20 November 2013
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Abstract

In this paper, we use Lyapunov direct method to analyze two identical Memristors systems and synchronization phenomena were discussed. The designed controllers were capable of making the time derivative of the Lyapunov’s negative definite functions where these results give guarantees of stability of the error dynamics at the origin and proved the results in form of theoretical and numerical ways. As the result, in both cases, one can see the synchronization phenomena.

DOI 10.11648/j.acm.20130206.14
Published in Applied and Computational Mathematics (Volume 2, Issue 6, December 2013)
Page(s) 130-136
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Synchronization; 4-D chaotic System and Lyapunov Direct Method

References
[1] L. O. Chua, Memristor - The missing circuit element, IEEE Trans. Circuit Theory 18 (1971).
[2] L.M. Pecora, T.L. Carroll: Synchronization in chaotic systems. Physical Review Letters. 64:821-824(1990).
[3] Vincent UE, Njah AN, Akinlade O, Solarin ART: Phase synchronization in undirectionally coupled chaotic ratchets . Chaos 14:1018-1025(2004).
[4] Vincent UE, Njah AN, Akinlade O, Solarin ART: Phase synchronization in bidirectionally coupled chaotic ratchets . Physica A.360:180-196(2006).
[5] M A Aziz-Alaoui, Synchronization of Chaos, université du Havre, Elsevier Ltd. 213-226, 2006.
[6] M.T.Yassen, Adaptive control and synchronization of a modified Chua's circuit system, Applied Mathematics and Computation 135 113-128, 2003.
[7] A. N. Njah and O.D. Sunday, Synchronization of Identical and Non-identical 4-D Chaotic Systems via Lyapunov Direct Method, International Journal of Nonlinear Science Vol.8 No.1,pp. 3-10, 2009.
[8] M. ITOH, MEMRISTOR OSCILLATORS, September, International Journal of Bifurcation and Chaos, Vol. 18, No. 11, 3183-3206 18, 2008.
[9] Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart and R. Stanley Williams, The missing memristor found, Vol 453 nature 06932 1 May 2008.
[10] B. Muthuswamy, Memristor Based Chaotic Circuits, Technical Report No.UCB/EECS-2009.
Author Information
  • University of Sulaimani, Faculty of Science and Science Education, School of Science, Department of Mathematics, Iraq

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  • APA Style

    Shko A. TAHIR. (2013). The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method. Applied and Computational Mathematics, 2(6), 130-136. https://doi.org/10.11648/j.acm.20130206.14

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    ACS Style

    Shko A. TAHIR. The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method. Appl. Comput. Math. 2013, 2(6), 130-136. doi: 10.11648/j.acm.20130206.14

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    AMA Style

    Shko A. TAHIR. The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method. Appl Comput Math. 2013;2(6):130-136. doi: 10.11648/j.acm.20130206.14

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  • @article{10.11648/j.acm.20130206.14,
      author = {Shko A. TAHIR},
      title = {The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method},
      journal = {Applied and Computational Mathematics},
      volume = {2},
      number = {6},
      pages = {130-136},
      doi = {10.11648/j.acm.20130206.14},
      url = {https://doi.org/10.11648/j.acm.20130206.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20130206.14},
      abstract = {In this paper, we use Lyapunov direct method to analyze two identical Memristors systems and synchronization phenomena were discussed. The designed controllers were capable of making the time derivative of the Lyapunov’s negative definite functions where these results give guarantees of stability of the error dynamics at the origin and proved the results in form of theoretical and numerical ways. As the result, in both cases, one can see the synchronization phenomena.},
     year = {2013}
    }
    

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