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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 758676, 10 pages
Amplitude Modulation and Synchronization of Fractional-Order Memristor-Based Chua's Circuit
1Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt
2NISC Research Center, Nile University, Egypt
3Department of Mathematics, Faculty of Science and Arts, Shaqra University, Saudi Arabia
4School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Received 19 July 2013; Accepted 14 October 2013
Academic Editor: Bashir Ahmad
Copyright © 2013 A. G. Radwan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press, San Diego, Calif, USA, 1999.
- L. Dorcak, Numerical Models for the Simulation of the Fractional-Order Control Systems, Technical University of Kosice, Kosice, Slovakia, 1994.
- A. Babakhani and D. Baleanu, “Existence and uniqueness of solution for a class of nonlinear fractional order differential equations,” Abstract and Applied Analysis, vol. 2012, Article ID 632681, 14 pages, 2012.
- T. Abdeljawad, B. Benli, and D. Baleanu, “A generalized q-mittag-leffler function by q-captuo fractional linear equations,” Abstract and Applied Analysis, vol. 2012, Article ID 546062, 11 pages, 2012.
- S. K. Han, C. Kerrer, and Y. Kuramoto, “Dephasing and burstling in coupled neural oscillators,” Physical Review Letters, vol. 75, pp. 3190–3193, 1995.
- K. Moaddy, A. G. Radwan, K. N. Salama, S. Momani, and I. Hashim, “The fractional-order modeling and synchronization of electrically coupled neuron systems,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3329–3339, 2012.
- A. G. Radwan, A. S. Elwakil, and A. M. Soliman, “Fractional-order sinusoidal oscillators: design procedure and practical examples,” IEEE Transactions on Circuits and Systems I, vol. 55, no. 7, pp. 2051–2063, 2008.
- A. G. Radwan, A. M. Soliman, and A. S. Elwakil, “First-order filters generalized to the fractional domain,” Journal of Circuits Systems & Computers, vol. 17, pp. 55–66, 2008.
- A. Shamim, A. G. Radwan, and K. N. Salama, “Fractional smith chart theory,” IEEE Microwave and Wireless Components Letters, vol. 21, no. 3, pp. 117–119, 2011.
- A. G. Radwan, “Stability analysis of the fractional-order RLC circuit,” Journal of Fractional Calculus and Applications, vol. 3, no. 1, pp. 1–15, 2012.
- A. G. Radwan, “Resonance and quality factor of the fractional RLC circuit,” IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. 3, no. 3, pp. 377–385, 2013.
- A. G. Radwan, K. Moaddy, K. N. Salama, S. Momani, and I. Hashim, “Control and switching synchronization of fractional order chaotic systems using active control technique,” Journal of Advanced Research, 2013.
- A. G. Radwan, S. K. Abd-El-Hafiz, and S. H. Abd-El-Haleem, “Image encryption in the fractional-order domain,” in Proceedings of the International Conference on Engineering and Technology (ICET '12), 2012.
- M. Feki, “An adaptive chaos synchronization scheme applied to secure communication,” Chaos, Solitons and Fractals, vol. 18, no. 1, pp. 141–148, 2003.
- K. Murali and M. Lakshmanan, “Secure communication using a compound signal from generalized synchronizable chaotic systems,” Physics Letters A, vol. 241, no. 6, pp. 303–310, 1998.
- T. Yang, “A survey of chaotic secure communication systems,” International Journal of Computational Cognition, vol. 2, no. 2, pp. 81–130, 2004.
- I. Wedekind and U. Parlitz, “Experimental observation of synchronization and anti-synchronization of chaotic low-frequency-fluctuations in external cavity semiconductor lasers,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 11, no. 4, pp. 1141–1147, 2001.
- J.-b. Liu, C.-f. Ye, S.-j. Zhang, and W.-t. Song, “Anti-phase synchronization in coupled map lattices,” Physics Letters A, vol. 274, no. 1-2, pp. 27–29, 2000.
- M.-C. Ho, Y.-C. Hung, and C.-H. Chou, “Phase and anti-phase synchronization of two chaotic systems by using active control,” Physics Letters A, vol. 296, no. 1, pp. 43–48, 2002.
- G.-H. Li and S.-P. Zhou, “Anti-synchronization in different chaotic systems,” Chaos, Solitons and Fractals, vol. 32, no. 2, pp. 516–520, 2007.
- S. Bhalekar and V. Daftardar-Gejji, “Antisynchronization of nonidentical fractional-order chaotic systems using active control,” International Journal of Differential Equations, vol. 2011, Article ID 250763, 13 pages, 2011.
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
- L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Physical Review A, vol. 44, no. 4, pp. 2374–2383, 1991.
- D. Bin, W. Jiang, and F. Xiangyang, “Chaotic synchronization with gap junction of multi-neurons in external electrical stimulation,” Chaos, Solitons and Fractals, vol. 25, no. 5, pp. 1185–1192, 2005.
- J. Yan and C. Li, “On chaos synchronization of fractional differential equations,” Chaos, Solitons & Fractals, vol. 32, no. 2, pp. 725–735, 2007.
- L. O. Chua, M. Itoh, L. Kocarev, and K. Eckert, “Chaos synchronization in Chua's circuit,” Journal of Circuits, Systems, and Computers, vol. 3, no. 1, pp. 93–108, 1993.
- C. Li and T. Zhou, “Synchronization in fractional-order differential systems,” Physica D, vol. 212, no. 1-2, pp. 111–125, 2005.
- Y. Yu, H.-X. Li, and Y. Su, “The synchronization of three chaotic fractional-order Lorenz systems with bidirectional coupling,” Journal of Physics, vol. 96, no. 1, Article ID 012113, 2008.
- Z. M. Odibat, N. Corson, M. A. Aziz-Alaoui, and C. Bertelle, “Synchronization of chaotic fractional-order systems via linear control,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 1, pp. 81–97, 2010.
- S. Bhalekar and V. Daftardar-Gejji, “Synchronization of different fractional order chaotic systems using active control,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, pp. 3536–3546, 2010.
- A. G. Radwan, K. Moaddy, and S. Momani, “Stability and non-standard finite difference method of the generalized Chua's circuit,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 961–970, 2011.
- I. Petráš, “Fractional-order memristor-based Chua's circuit,” IEEE Transactions on Circuits and Systems II, vol. 57, no. 12, pp. 975–979, 2010.
- G. Hussian, M. Alnaser, and S. Momani, “Non-standard discretization of fractional differential equations,” in Proceedings of the 8th seminar of differential equations and dynamical systems, 2008.
- Applications of Nonstandard Finite Difference Schemes, World Scientific Publishing, River Edge, NJ, USA, 2000.
- A. G. Radwan, M. A. Zidan, and K. N. Salama, “HP memristor mathematical model for periodic signals and DC,” in Proceedings of the IEEE International Midwest Symposium on Circuits and Systems, pp. 861–864, 2010.
- A. Talukdar, A. G. Radwan, and K. N. Salama, “Non linear dynamics of memristor based 3rd order oscillatory system,” Microelectronics Journal, vol. 43, no. 3, pp. 169–175, 2012.
- A. G. Radwan, M. A. Zidan, and K. N. Salama, “HP Memristor mathematical model for periodic signals and DC,” in Proceedings of the 53rd IEEE International Midwest Symposium on Circuits and Systems (MWSCAS '10), pp. 861–864, Seattle, Wash, USA, August 2010.
- A. G. Radwan, M. A. Zidan, and K. N. Salama, “On the mathematical modeling of Memristors,” in Proceedings of the International Conference on Microelectronics (ICM '10), pp. 284–287, December 2010.
- W. Hahn, Stability of Motion, Springer, New York, NY, USA, 1967.
- G. Kolumbán, M. P. Kennedy, and L. O. Chua, “The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization,” IEEE Transactions on Circuits and Systems I, vol. 45, no. 11, pp. 1129–1140, 1998.
- N. J. Corron and D. W. Hahs, “A new approach to communications using chaotic signals,” IEEE Transactions on Circuits and Systems I, vol. 44, no. 5, pp. 373–382, 1997.