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Dynamic behaviours and control of fractional-order memristor-based system

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Abstract

Dynamics of fractional-order memristor circuit system and its control are investigated in this paper. With the help of stability theory of fractional-order systems, stability of its equilibrium points is analysed. Then, the chaotic behaviours are validated using phase portraits, the Lyapunov exponents and bifurcation diagrams with varying parameters. Furthermore, some conditions ensuring Hopf bifurcation with varying fractional orders and parameters are determined, respectively. By using a stabilization theoremproposed newly for a class of nonlinear systems, linear feedback controller is designed to stabilize the fractional-order system and the corresponding stabilization criterion is presented. Numerical simulations are given to illustrate and verify the effectiveness of our analysis results.

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References

  1. L O Chua, IEEE Trans. Circuit Theory 18, 507 (1971)

  2. D Strukov, G S Snider, D R Stewart and R S Williams, Nature 453, 80 (2008)

  3. Y V Pershin and M D Ventra, Neural Networks 23, 881 (2010)

  4. Y V Pershin, S L Fontaine and M D Ventra, Phys. Rev. E 80, 021926 (2009)

  5. J Borghetti, G S Snider, P J Kuekes and J J Yang, Nature 464, 873 (2010)

  6. K Eshraghian, K R Cho, O Kavehei, S K Kang, D Abbott and S M S Kang, IEEE Trans. VLSI Syst. 19, 1407 (2011)

  7. B Bao, Z Ma, J Xu, Z Liu and Q Xu, Int. J. Bifurcat. Chaos 21, 2629 (2011)

  8. M Itoh and L O Chua, Int. J. Bifurcat. Chaos 18, 3183 (2008)

  9. B Muthuswamy and L O Chua, Int. J. Bifurcat. Chaos 20, 1567 (2010)

  10. C Fernando, A Alon and G Marco, IEEE Trans. Circuits Syst. I 58, 1323 (2011)

  11. B Muthuswamy, Int. J. Bifurcat. Chaos 20, 1335 (2010)

  12. Y V Pershin and M D Ventra, Neural Netw. 23, 881 (2010)

  13. A Buscarino, L Fortuna, M Frasca, L V Gambuzza and G Sciuto, Int. J. Bifurcat. Chaos 22, 1250070 (2012)

  14. A Buscarino, L Fortuna, M Frasca and L V Gambuzza, Chaos 22, 023136 (2012)

  15. C Li and Y Tong, Pramana – J. Phys. 80, 583 (2013)

  16. Y Chai, L P Chen, R C Wu and J Dai, Pramana – J. Phys. 80, 449 (2013)

  17. J Wang, L Zeng and Q Ma, Pramana – J. Phys. 76, 385 (2011)

  18. T T Hartley, C F Lorenzo and Q H Killory, IEEE Trans. Circuits Syst. I 42, 485 (1995)

  19. Z M Ge and C Y Ou, Chaos, Solitons and Fractals 34, 262 (2007)

  20. C P Li and G J Peng, Chaos, Solitons and Fractals 22, 443 (2004)

  21. J G Lu, Phys. Lett. A 354, 305 (2006)

  22. X Y Wang and M J Wang, Chaos 17, 033106 (2007)

  23. W C Chen, Chaos, Solitons and Fractals 36, 1305 (2008)

  24. E Kaslik and S Sivasundaram, Neural Networks 32, 245 (2012)

  25. I Petras, IEEE Trans. Circuits Syst. II 57, 975 (2010)

  26. I Podlubny, Fractional differential equations (Academic Press, San Diego, 1999)

  27. L P Chen, Y G He, Y Chai and R C Wu, Nonlinear Dyn. 75, 633 (2014)

  28. K Diethelm, N J Ford and A D Freed, Nonlinear Dyn. 29, 3 (2002)

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Acknowledgements

This work was supported by the National Natural Science Funds of China for Distinguished Young Scholar under Grant (No. 50925727), the National Natural Science Funds of China (Nos 61403115 and 61374135), the National Defense Advanced Research Project Grant (No. C1120110004), the Key Grant Project of Chinese Ministry of Education under Grant (No. 313018), the Anhui Provincial Science and Technology Foundation of China under Grant (No. 1301022036) and the 211 project of Anhui University (No. KJJQ1102).

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China

    LIPING CHEN & YIGANG HE

  2. Chongqing Special Equipment Inspection and Research Institute, Chongqing, 401121, China

    XIAO LV

  3. School of Mathematics, Anhui University, Hefei, 230039, China

    RANCHAO WU

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  1. LIPING CHEN
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  2. YIGANG HE
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Correspondence to LIPING CHEN.

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CHEN, L., HE, Y., LV, X. et al. Dynamic behaviours and control of fractional-order memristor-based system. Pramana - J Phys 85, 91–104 (2015). https://doi.org/10.1007/s12043-014-0880-9

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  • DOI: https://doi.org/10.1007/s12043-014-0880-9

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