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Dynamics of a fractional-order voltage-controlled locally active memristor

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Abstract

In this paper, a fractional-order locally active memristor is proposed based on the definition of fractional derivative. It is found that the side lobe area of the pinched hysteretic curve of the memristor changes with the fractional-order value, and the side lobe’s area of the fractional-order memristor is greater than that of the memristor with integer order, meaning that the memory of the fractional-order memristor is stronger than that of the memristor with integer order. It is proved by the dynamic rout map (DRM) that the fractional-order memristor possesses continuous memory. The pinched hysteresis, memristance and power characteristics which vary with the fractional order are compared and analysed in detail. Furthermore, we use the memristor to construct a fractional-order chaotic circuit, which can exhibit continuous chaotic motion in the range of \(0.75<\) fractional order \(\alpha < 1\) and various coexisting attractors. We also show that the lower fractional order causes higher complexity of the fractional-order chaotic system using different methods, such as Lyapunov exponent spectrum, bifurcation diagram, spectral entropy and C0 complexity method. Finally, the circuit simulations of the fractional-order chaotic circuit are realised, demonstrating the validity of the mathematical model and the theoretical analysis.

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References

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Y J Yu and Z H Wang, Int. J. Bifurc. Chaos 28, 1850091 (2018)

    Article  Google Scholar 

  4. H B Bao and J D Cao, Neural Netw. 1, 63 (2015)

    Google Scholar 

  5. J T Machado, Commun. Nonlin. Sci. Numer. Simulat. 264, 18 (2013)

    Google Scholar 

  6. D Y Xue and C N Zhao, Control Theory Appl. 24, 771 (2007)

    Google Scholar 

  7. Y J Yu and Z H Wang, Acta Phys. Sin. 64, 238401 (2015)

    Article  Google Scholar 

  8. I Petráás̆ and Y Q Chen, IEEE International Carpathian Control Conference (2012)

  9. M E Fouda and A G Radwan, J. Fract. Calc. Appl. 4, 1 (2017)

    Google Scholar 

  10. M E Fouda and A G Radwan, Circuits Syst. Signal Process 34, 961 (2015)

    Article  Google Scholar 

  11. E M Hamed, M E Fouda and A G Radwan, IEEE International Symposium on Circuits and Systems (2018)

  12. A H Elsafty, E M Hamed, M E Fouda, L A Said and A H Madian, 7th International Conference on Modern Circuits and Systems Technologies (MOCAST) (2018)

  13. J Wu, G Y Wang, H H C Iu, Y R Shen and W Zhou, Entropy 21, 955 (2019)

    Article  ADS  Google Scholar 

  14. D Cafagna and G Grassi, Int. J. Bifurc. Chaos 18, 615 (2008)

    Article  Google Scholar 

  15. I Grigorenko and E Grigorenko, Phys. Rev. Lett. 91, 34101 (2003)

    Article  ADS  Google Scholar 

  16. V T Pham, S T Kingni, C Volos, S Jafari and T Kapitaniak, Int. J. Electron. Commun. 78, 220 (2017)

    Article  Google Scholar 

  17. Y Xu, H Wang, Y Li and B Pei, Commun. Nonlin. Sci Numer. Simulat. 19, 3735 (2014)

    Article  ADS  Google Scholar 

  18. P Muthukumar, P Balasubramaniam and K Ratnavelu, Nonlinear Dyn. 80, 1883 (2015)

    Article  Google Scholar 

  19. D Cafagna and G Grassi, Nonlinear Dyn. 70, 1185 (2012)

    Article  Google Scholar 

  20. I Petrás̆, IEEE Trans. Circuits Syst. II: Express Br. 57, 975 (2010)

    Article  Google Scholar 

  21. N N Yang, C Xu, C J Wu and R Jia, Int. J. Bifurc. Chaos 27, 1750199 (2017)

    Article  Google Scholar 

  22. L O Chua, Int. J. Bifurc. Chaos 15, 3435 (2005)

    Article  MathSciNet  Google Scholar 

  23. L O Chua, Semicond. Sci. Technol. 29, 104001 (2014)

    Article  ADS  Google Scholar 

  24. S P Adhikari, M P Sah, H Kim and L O Chua, IEEE Trans. Circuits Syst. I: Regul. Pap. 60, 3008 (2013)

    Article  Google Scholar 

  25. M D Pickett and R S Williams, Nanotechno l. 23, 215202 (2012)

    Article  ADS  Google Scholar 

  26. S Kumar, J P Strachan and R S Williams, Nature 548, 318 (2017)

    Article  ADS  Google Scholar 

  27. B R Xu, G Y Wang, X Y Wang and H H C Iu, Pramana – J. Phys. 93, 1 (2019)

    Article  ADS  Google Scholar 

  28. K H Sun, Principle and technology of chaotic secure communication (Tsinghua University Press, Beijing, 2015)

    Google Scholar 

  29. N Heymans and I Podlubny, Rheol. Acta 45, 5 (2006)

    Article  Google Scholar 

  30. R Agarwal, S Hristova and D O Regan, Mathematics 8, 4 (2020)

    Google Scholar 

  31. C Li, D Qian and Y Q Chen, Disc. Dyn. Nat. Soc. 10, 1155 (2011)

    Google Scholar 

  32. D Biolek, Z Biolek and V Biolková, Electron. Lett. 50, 74 (2014)

    Article  ADS  Google Scholar 

  33. Z Biolek, D Biolek and V Biolková, IEEE Trans. Circuits Syst. II: Express Br. 59, 607 (2012)

    Article  Google Scholar 

  34. R Hilfer, Application of fractional calculus in physics (Universität Mainz and Universität Stuttgart, Germany, 2000)

    Book  Google Scholar 

  35. S Westerlund, Phys. Scr. 43, 174 (1991)

    Article  ADS  Google Scholar 

  36. R Barboza and L O Chua, Int. J. Bifurc. Chaos 18, 943 (2008)

    Article  Google Scholar 

  37. L P Chen, Y G He, X Lv and R C Wu, Pramana – J. Phys. 85, 91 (2015)

  38. J P Singh and B K Roy, Chaos Solitons Fractals 92, 73 (2016)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos 61771176 and 61801154), and in part by the Zhejiang Provincial Natural Science Foundation of China under Grant LY20F010008. The authors would like to acknowledge Yujiao Dong who made great contributions to the derivtion of equations, verification of theories, data analyses, revisions of almost all figures, and the latex format of the final manuscript.

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Authors and Affiliations

  1. Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou,  310018, China

    weiyang wang, guangyi wang, jiajie YING, gongzhi liu & yan liang

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  1. weiyang wang
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  2. guangyi wang
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  3. jiajie YING
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  4. gongzhi liu
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Correspondence to guangyi wang.

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wang, w., wang, g., YING, j. et al. Dynamics of a fractional-order voltage-controlled locally active memristor. Pramana - J Phys 96, 109 (2022). https://doi.org/10.1007/s12043-022-02354-7

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  • DOI: https://doi.org/10.1007/s12043-022-02354-7

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