Dynamics and Synchronization of Memristor-Based Fractional-Order System


A memristor-based fractional order circuit derived from Chua’s topology is presented. The dynamic properties of this circuit such as phase trajectories, time evolution characteristics of state variables are analyzed through the approximation method of fractional order operator. In addition, it clearly describes the relationships between the impedance variation of the memristor and the varying mobility of the doped region of the memristor in different circuit parameters. Finally, a periodic memristor-based system driven by another chaotic memristor-based fractional order system is synchronized to chaotic state via the linear error feedback technique.

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H. Deng and Q. Wang, "Dynamics and Synchronization of Memristor-Based Fractional-Order System," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 4, 2013, pp. 223-227. doi: 10.4236/ijmnta.2013.24031.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] L. O. Chua, “Memristor—The Missing Circuit Element,” IEEE Transactions on Circuit Theory, Vol. 18, No. 5, 1971, pp. 507-519.
[2] D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, “The Missing Memristor Found,” Nature, Vol. 453, No. 7191, 2008, pp. 80-83.
http://dx.doi.org/10.1038/nature 06932
[3] K. C. Liu, W. H. Tzeng, K. M. Chang, et al. “The Resistive Switching Characteristics of a Ti/Gd2O3/Pt RRAM Device,” Microelectronics Reliability, Vol. 50, No. 5, 2010, pp. 670-673.
[4] K. S. Vasu, S. Sampath and A. K. Sood, “Nonvolatile Unipolar Resistive Switching in Ultrathin Films of Graphene and Carbon Nanotubes,” Solid State Communications, Vol. 151, No. 16, 2011, pp. 1084-1087.
[5] A. Kiazadeh, H. L. Gomes, A. M. R. Costa, et al., “Intrinsic and Extrinsic Resistive Switching in a Planar Diode Based on Silver Oxide Nanoparticles,” Thin Solid Films, Vol. 522, 2012, pp. 407-411.
[6] B. Muthuswamy and P. P. Kokate, “Memristor-Based Chaotic Circuits,” IETE Technical Review, Vol. 26, No. 6, 2009, pp. 417-429.
[7] Y. V. Pershin and M. Di Ventra, “Experimental Demonstration of Associative Memory with Memristive Neural Networks,” Neural Networks, Vol. 23, No. 7, 2010, pp. 881-886. http://dx.doi.org/10.1016/j.neunet.2010.05.001
[8] F. Z. Wang, H. Na, S. Wu, et al., “Delayed Switching in Memristors and Memristive Systems,” IEEE Electron Device Letters, Vol. 31, No. 7, 2010, pp. 755-757.
[9] 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, 2012, pp. 169-175.
[10] A. Buscarino, L. Fortuna, M. Frasca and L. V. Gambuzza, “A Chaotic Circuit Based on Hewlett-Packard Memristor,” Chaos, Vol. 22, No. 2, 2012, Article ID: 023136.
[11] I. Petrás, “Fractional-Order Memristor-Based Chua’s Circuit,” IEEE Transactions on Circuits and Systems—II: Express Briefs, Vol. 57, No. 12, 2010, pp. 975-979.
[12] S. P. Wen, Z. G. Zheng and T. W. Huang, “Adaptive Synchronization of Memristor-Based Chua’s Circuits,” Physics Letters A, Vol. 376, No. 44, 2012, pp. 2775-2780.
[13] Y. N. Joglekar and S. J. Wolf, “The Elusive Memristor: Properties of Basic Electrical Circuits,” European Journal of Physics, Vol. 30, No. 4, 2009, pp. 661-675.
[14] Z. Biolek, D. Biolek and V. Biolkova, “SPICE Model of Memristor with Nonlinear Dopant Drift,” Radioengineering, Vol. 18, No. 2, 2009, pp. 210-214.
[15] I. Podlubny, “Fractional Differential Equations,” Academic Press, San Diego, 1999.
[16] T. T. Hartley, C. F. Lorenzo and H. K. Qammar, “Chaos in a Fractional Order Chua’s System,” IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications, Vol. 42, No. 8, 1995, pp. 485-490.

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