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Bursting oscillations and bifurcation mechanism in a fully integrated piecewise-smooth chaotic system

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Abstract

This paper aims to show and investigate bursting oscillator and bifurcation phenomena in a piecewise-smooth memristor-based Shimizu–Morioka (SM) system. First, a piecewise-smooth nonlinear system is built. Second, considering the memory characteristic of the memristor and the formation of the bursting oscillations circuit, a memristor and a periodic excitation are introduced into the system which leads to the piecewise-smooth memristor-based systems with a single slow variable. As the slow variable changes periodically in different scopes, we discover intricate bursting oscillation phenomena, namely, asymmetric Fold/Fold bursting, damped oscillation-sliding, asymmetric Fold/Fold-delayed supHopf/supHopf bursting, compressed oscillation phenomenon within the limit cycle, random bursting, double loop oscillations and so on. To make the circuit low power consumption and portable in practice, it is fully integrated. In the course of the study, it is found that the properties of the nominal equilibrium orbits, limit cycles, and the non-smooth boundary contribute to the bursting. Finally, a fully integrated circuit is designed and the accuracy of the study is verified by some circuit simulation results.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited.

References

  1. H. Hetzler, Nonlinear Dyn. 69, 601–14 (2012)

    Article  MathSciNet  Google Scholar 

  2. R. Zhang, M. Peng, Z.D. Zhang, Q.S. Bi, Chin. Phys. B 27(11), 416–22 (2018)

    Google Scholar 

  3. Z.D. Zhang, B.B. Liu, Q.S. Bi, Nonlinear Dyn. 79(1), 195–203 (2015)

    Article  Google Scholar 

  4. Q.S. Bi, X.K. Chen, J. Kurths, Z.D. Zhang, Nonlinear Dyn. 85(4), 2233–45 (2016)

    Article  Google Scholar 

  5. X.H. Li, J.Y. Hou, Int. J. Non-Linear Mech. 81, 165–76 (2016)

    Article  ADS  Google Scholar 

  6. L. Wang, X.S. Yang, Nonlinear Dyn. 97(4), 2469–81 (2019)

    Article  Google Scholar 

  7. D.H. Li, H.B. Chen, J.H. Xie, Int. J. Bifurc. Chaos 29(4), 1950051 (2019)

    Article  Google Scholar 

  8. N. Ramou, Russ. J. Nondestr. Test. 55(2), 155–61 (2019)

    Article  Google Scholar 

  9. R. Cristiano, D.J. Pagano, J. Nonlinear Sci. 29(3), 2845–75 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  10. S.T. Kingni, L. Keuninckx, P. Woafo, G. Van der Sande, J. Danckaert, Nonlinear Dyn. 73(1–2), 1111–23 (2013)

    Article  Google Scholar 

  11. A.M.N. Kiss, B. Marx, G. Mourot, G. Schutz, J. Ragot, Control. Eng. Pract. 19(11), 1354–62 (2011)

    Article  Google Scholar 

  12. M. Kess, C. Brüning, V. Engel, Chem. Phys. 442(11), 26–30 (2014)

    Article  Google Scholar 

  13. Q.S. Bi, Sci. China Technol. Sci. 53(2), 748–60 (2010)

    Article  ADS  Google Scholar 

  14. B.R. Miller, A.G. Walker, A.S. Shah, S.J. Barton, G.V. Rebec, J. Neurophysiol. 100(4), 2205–16 (2008)

    Article  Google Scholar 

  15. Z.D. Zhang, Y.Y. Li, Q.S. Bi, Phys. Lett. A 377(13), 975–80 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  16. E.M. Izhikevich, Int. J. Bifurc. Chaos 10(06), 1171–266 (2000)

    Article  MathSciNet  Google Scholar 

  17. D. Cafagna, G. Grassi, Math Probl. Eng. 2013, 1–7 (2013)

    Article  Google Scholar 

  18. V.T. Pham, A. Ouannas, C. Volos, T. Kapitaniak, AEU-Int. J. Electron. Commun. 86, 69–76 (2018)

    Article  Google Scholar 

  19. G.S. Yi, J. Wang, X.L. Wei, B. Deng, H.Y. Li, C.X. Han, Appl. Math. Comput. 231, 100–10 (2014)

    MathSciNet  Google Scholar 

  20. F. Grgoire-Lacoste, V. Jacquemet, A. Vinet, Math. Biosci. 250, 10–25 (2014)

    Article  MathSciNet  Google Scholar 

  21. L.O. Chua, Memristor-the missing circuit element (IEEE Transactions, 1971) 507-19

  22. Q.W. Tan, Y.C. Zeng, Z.J. Li, Nonlinear Dyn. 94(3), 1585–602 (2018)

    Article  Google Scholar 

  23. Zbigniew Galias, IEEE Trans. Circ. Syst. II Exp. Briefs 65(5), 637–41 (2018)

    Google Scholar 

  24. J. Kengne, A. Nguomkam Negou, D. Tchiotsop, Nonlinear Dyn. 88, 2589–608 (2017)

    Article  Google Scholar 

  25. C. Zhou, C.H. Wang, Y. Sun, W. Yao, Neurocomputing 403, 225–32 (2020)

    Article  Google Scholar 

  26. H. Bao, N. Wang, B.C. Bao, M. Chen, P.P. Jin, G.Y. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264–75 (2018)

  27. Q.H. Fu, J.Y. Cai, S.M. Zhong, Int. J. Control Autom. Syst. 17, 2666–76 (2019)

  28. X.T. Min, X.Y. Wang, P.F. Zhou, S.M. Yu, H.H.C. Iu, IEEE Access 99, 124641–46 (2019)

    Article  Google Scholar 

  29. Q. Lai, Z.Q. Wan, P.D.K. Kuate, H. Fotsin, Commun. Nonlinear Sci. Numer. Simul. 89, 105341 (2020)

    Article  MathSciNet  Google Scholar 

  30. N.H. Alombah, H. Fotsin, K. Romanic, Int. J. Bifurc. Chaos Appl. Sci. Eng. 27(05), 1750067 (2017)

    Article  Google Scholar 

  31. N. Wang, G.S. Zhang, H. Bao, Nonlinear Dyn. 97, 1477–94 (2019)

    Article  Google Scholar 

  32. Z.H. Wen, Z.J. Li, X. Li, Chaos. Solitons & Fractals 128, 58–70 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  33. B.C. Bao, P. Wu, H. Bao, H.G. Wu, X. Zhang, M. Chen, Chaos Solitons & Fractals 109, 146–53 (2018)

    Article  ADS  Google Scholar 

  34. H.G. Wu, B.C. Bao, Z. Liu, Q. Xu, P. Jiang, Nonlinear Dyn. 83, 893–903 (2015)

    Article  Google Scholar 

  35. J. Jin, L.V. Zhao, J. Circ. Syst. Comput. 27(10), 1850155 (2018)

    Article  Google Scholar 

  36. J. Jin, Microelectron. J. 75, 27–34 (2018)

    Article  Google Scholar 

  37. X.W. Jiang, X.Y. Chen, T.W. Huang, H.C. Yan, IEEE Trans. Circ. Syst. II Express Brief 99, 1 (2020)

    Google Scholar 

  38. X.W. Jiang, X.Y. Chen, M. Chi, J. Chen, Appl. Math. Comput. 370, 124906 (2020)

    MathSciNet  Google Scholar 

  39. X.W. Jiang, X.S. Zhan, Z.H. Guan, X.H. Zhang, L. Yu, J. Franklin Inst. 352(1), 1–15 (2015)

    Article  MathSciNet  Google Scholar 

  40. B. Razavi, Design of Analog CMOS Integrated Circuits (McGraw-Hill Education, 2016) 389

  41. C. Sawigun, J. Mahattanakul, IEEE International Symposium on Circuits and Systems 2318–21 (2008)

Download references

Acknowledgements

This work was supported by the National key R & D program of China under Grant 2018AAA0103300.

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Authors and Affiliations

  1. College of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Minglin Ma, Yingjun Fang, Zhijun Li & Mengjiao Wang

  2. School of Engineering and Technology, University of Hertfordshire, Hatfield, AL10 9AB, UK

    Yichuang Sun

Authors
  1. Minglin Ma
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  2. Yingjun Fang
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  3. Zhijun Li
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  4. Yichuang Sun
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  5. Mengjiao Wang
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Contributions

All authors contributed equally to this work. MLM performed the MATLAB simulations. YJF wrote the main paper and YCS polished the manuscript. ZJL designed and implemented the simulation of the integrated circuit. MJW carried out the drawing of XPPAUT. All authors discussed the results and commented on the manuscript at all stages.

Corresponding author

Correspondence to Yingjun Fang.

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Ma, M., Fang, Y., Li, Z. et al. Bursting oscillations and bifurcation mechanism in a fully integrated piecewise-smooth chaotic system. Eur. Phys. J. Spec. Top. 230, 1737–1749 (2021). https://doi.org/10.1140/epjs/s11734-021-00128-7

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