Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2017 (2017), Article ID 5186714, 10 pages
https://doi.org/10.1155/2017/5186714
Research Article

Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

1School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, China
3Key Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges University, Chongqing 404100, China

Correspondence should be addressed to Limin Zou

Received 14 April 2017; Revised 26 June 2017; Accepted 6 November 2017; Published 5 December 2017

Academic Editor: Sigurdur F. Hafstein

Copyright © 2017 Limin Zou 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.

Linked References

  1. L. O. Chua, “Memristor—the missing circuit element,” IEEE Transactions on Circuit Theory, vol. 18, no. 5, pp. 507–519, 1971. View at Publisher · View at Google Scholar
  2. “Memristor-Wikipedia,” https://en.wikipedia.org/wiki/Memristor.
  3. D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature, vol. 453, pp. 80–83, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. V. Pershin, S. La Fontaine, and M. Di Ventra, “Erratum: Memristive model of amoeba learning,” Physical Review E, vol. 82, no. 1, 2010. View at Publisher · View at Google Scholar
  5. A. Afifi, A. Ayatollahi, and F. Raissi, “Implementation of biologically plausible spiking neural network models on the memristor crossbar-based CMOS/nano circuits,” in Proceedings of the ECCTD 2009 - European Conference on Circuit Theory and Design Conference Program, pp. 563–566, Turkey, August 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. S. Williams, “‘Memristive’ switches enable “stateful” logic operations via material implication,” Nature, vol. 464, no. 7290, pp. 873–876, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. S. H. Jo, T. Chang, I. Ebong, B. B. Bhadviya, P. Mazumder, and W. Lu, “Nanoscale memristor device as synapse in neuromorphic systems,” Nano Letters, vol. 10, no. 4, pp. 1297–1301, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Itoh and L. O. Chua, “Memristor oscillators,” International Journal of Bifurcation and Chaos, vol. 18, no. 11, pp. 3183–3206, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. B. Muthuswamy and P. Kokate, “Memristor-based chaotic circuits,” IETE Technical Review, vol. 26, no. 6, pp. 415–426, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Lin and H. Wang, “Image encryption based on chaos with PWL memristor in Chua's circuit,” in Proceedings of the 2009 International Conference on Communications, Circuits and Systems (ICCCAS), pp. 964–968, Milpitas, Ca, USA, July 2009. View at Publisher · View at Google Scholar
  11. T. Yang, Impulsive Control Theory, Springer, Berlin , Germany, 2001. View at MathSciNet
  12. T. Yang, L.-B. Yang, and C.-M. Yang, “Impulsive control of Lorenz system,” Physica D: Nonlinear Phenomena, vol. 110, no. 1-2, pp. 18–24, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Sun, Y. Zhang, and Q. Wu, “Impulsive control for the stabilization and synchronization of Lorenz systems,” Physics Letters A, vol. 298, no. 2-3, pp. 153–160, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Z. Ai and C. Chen, “Asymptotic stability analysis and design of nonlinear impulsive control systems,” Nonlinear Analysis: Hybrid Systems, vol. 24, pp. 244–252, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. C. Li, X. Yu, Z.-W. Liu, and T. Huang, “Asynchronous impulsive containment control in switched multi-agent systems,” Information Sciences, vol. 370, pp. 667–679, 2016. View at Publisher · View at Google Scholar · View at Scopus
  16. X. Yang, J. Cao, and J. Qiu, “Pth moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control,” Neural Networks, vol. 65, pp. 80–91, 2015. View at Publisher · View at Google Scholar · View at Scopus
  17. X. Yang and J. Lu, “Finite-time synchronization of coupled networks with Markovian topology and impulsive effects,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 61, no. 8, pp. 2256–2261, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. Q. Song, H. Yan, Z. Zhao, and Y. Liu, “Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects,” Neural Networks, vol. 79, pp. 108–116, 2016. View at Publisher · View at Google Scholar
  19. Q. Song, H. Yan, Z. Zhao, and Y. Liu, “Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays,” Neural Networks, vol. 81, pp. 1–10, 2016. View at Publisher · View at Google Scholar · View at Scopus
  20. W. M. Haddad, V. Chellaboina, and S. G. Nersesov, Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, USA, 2006. View at MathSciNet
  21. T. Ma, Impulsive Control and Synchronization, Science Press, Beijing, China, 2016.
  22. B. Muthuswamy, “Implementing memristor based chaotic circuits,” International Journal of Bifurcation and Chaos, vol. 20, no. 5, pp. 1335–1350, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. S. J. Yang, C. D. Li, and T. W. Huang, “Impulsive control and synchronization of memristor-based chaotic circuits,” International Journal of Bifurcation and Chaos, vol. 24, no. 12, Article ID 1450162, 12 pages, 2014. View at Publisher · View at Google Scholar
  24. T. D. Ma and F. Y. Zhao, “Impulsive stabilization of a class of nonlinear system with bounded gain error,” Chinese Physics B, vol. 23, no. 12, Article ID 120504, 2014. View at Publisher · View at Google Scholar · View at Scopus