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.
Published in | Applied and Computational Mathematics (Volume 2, Issue 6) |
DOI | 10.11648/j.acm.20130206.14 |
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), 2013. Published by Science Publishing Group |
Synchronization; 4-D chaotic System and Lyapunov Direct Method
[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. |
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
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
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
@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://article.sciencepublishinggroup.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} }
TY - JOUR T1 - The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method AU - Shko A. TAHIR Y1 - 2013/11/20 PY - 2013 N1 - https://doi.org/10.11648/j.acm.20130206.14 DO - 10.11648/j.acm.20130206.14 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 130 EP - 136 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20130206.14 AB - 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. VL - 2 IS - 6 ER -