Advertisement

The European Physical Journal Special Topics

, Volume 228, Issue 10, pp 1943–1950 | Cite as

Detecting bifurcation points in a memristive neuron model

  • Yongjian Liu
  • Fahimeh NazarimehrEmail author
  • Abdul Jalil M. Khalaf
  • Ahmed Alsaedi
  • Tasawar Hayat
Regular Article
  • 24 Downloads
Part of the following topical collections:
  1. Memristor-based Systems: Nonlinearity, Dynamics and Applications

Abstract

In this paper, bifurcations of a memristive neuron model are analyzed. The system shows different limit cycles and chaotic attractors by varying external current. The focus of this paper is finding bifurcation points of the system and predicting them using critical slowing down indicators. The system has different tipping points such as transition from a period-2 limit cycle to period-3 limit cycle, period-3 limit cycle to period-6 limit cycle and limit cycle to chaos. Two critical slowing down indicators have been used to predict tipping points of the system. The first critical slowing down indicator is autocorrelation at lag-1 which cannot indicate bifurcation points of the system. The second one is Lyapunov exponent which shows acceptable results in prediction of bifurcation points of the memristive neuron model.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D.W. Crevier, M. Meister, J. Neurophysiol. 79, 1869 (1998)CrossRefGoogle Scholar
  2. 2.
    T. Quail, N. McVicar, M. Aguilar, M.-Y. Kim, A. Hodge, L. Glass, A. Shrier, Chaos: Interdiscip. J. Nonlinear Sci. 22, 033140 (2012)CrossRefGoogle Scholar
  3. 3.
    Y. Fan, A.V. Holden, Chaos Solitons Fractals 3, 439 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    S. Jafari, S.M.R. Hashemi Golpayegani, S. Gharibzadeh, Front. Comput. Neurosci. 7, 121 (2013)CrossRefGoogle Scholar
  5. 5.
    Z.-H. Guan, C.-Y. Chen, G. Feng, T. Li, I.E.E.E. Trans, Circuits Syst. I: Regul. Pap. 60, 189 (2013)CrossRefGoogle Scholar
  6. 6.
    X.-W. Zhao, B. Hu, Z.-H. Guan, C.-Y. Chen, M. Chi, X.-H. Zhang, IET Control Theor. Appl. 10, 2093 (2016)CrossRefGoogle Scholar
  7. 7.
    R. Wang, K. Mei, C. Chen, Y. Li, H. Mei, Z. Yu, J. Control Theor. Appl. 10, 309 (2012)CrossRefGoogle Scholar
  8. 8.
    C.-Y. Chen, Z.-H. Guan, M. Chi, Y. Wu, R.-Q. Liao, X.-W. Jiang, J. Franklin Inst. 354, 3120 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    C.-Y. Chen, W.-H. Gui, Z.-H. Guan, R.-L. Wang, S.-W. Zhou, Neurocomputing 226, 101 (2017)CrossRefGoogle Scholar
  10. 10.
    S. Jafari, Z. Ansari, S.M.R. Hashemi Golpayegani, S. Gharibzadeh, J. Neuropsychiatry Clin. Neurosci. 25, E05 (2013)CrossRefGoogle Scholar
  11. 11.
    J.C. Sprott, Chaos and time-series analysis (Oxford University Press, Oxford, 2003)Google Scholar
  12. 12.
    M. Scheffer, S.R. Carpenter, T.M. Lenton, J. Bascompte, W. Brock, V. Dakos, M. Pascual, Science 338, 344 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    M. Scheffer, J. Bascompte, W.A. Brock, V. Brovkin, S.R. Carpenter, V. Dakos, G. Sugihara, Nature 461, 53 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    F. Nazarimehr, S. Jafari, S.M.R.H. Golpayegani, J. Sprott, Nonlinear Dyn. 88, 1493 (2017)CrossRefGoogle Scholar
  15. 15.
    F. Nazarimehr, S. Jafari, S.M.R. Hashemi Golpayegani, M. Perc, J.C. Sprott, Chaos: Interdiscip. J. Nonlinear Sci. 28, 073102 (2018)CrossRefGoogle Scholar
  16. 16.
    V. Dakos, S.R. Carpenter, W.A. Brock, A.M. Ellison, V. Guttal, A.R. Ives, M. Scheffer, PloS One 7, e41010 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Q. Lai, A. Akgul, X.-W. Zhao, H. Pei, Int. J. Bifurc. Chaos 27, 1750142 (2017)CrossRefGoogle Scholar
  18. 18.
    Q. Lai, S. Chen, Int. J. Bifurc. Chaos 26, 1650177 (2016)CrossRefGoogle Scholar
  19. 19.
    Q. Lai, T. Nestor, J. Kengne, X.-W. Zhao, Chaos Solitons Fractals 107, 92 (2018)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Q. Lai, S. Chen, Optik-Int. J. Light Electron Opt. 127, 3000 (2016)CrossRefGoogle Scholar
  21. 21.
    Q. Lai, S. Chen, J. Int, Control, Autom. Syst. 14, 1124 (2016)CrossRefGoogle Scholar
  22. 22.
    Q. Lai, L. Wang, Optik 127, 5400 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    L. Chua, I.E.E.E. Trans, Circuit Theory 18, 507 (1971)CrossRefGoogle Scholar
  24. 24.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    Y. Zhang, G. Kong, J. Yu, Y. Chu, Phys. Lett. A 372, 5979 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    B. Bao, T. Jiang, G. Wang, P. Jin, H. Bao, M. Chen, Nonlinear Dyn. 89, 1 (2017)CrossRefGoogle Scholar
  27. 27.
    B. Bao, P. Wu, H. Bao, Q. Xu, M. Chen, Chaos Solitons Fractals 106, 161 (2018)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Y. Zhang, G. Kong, J. Yu, Phys. Lett. A 373, 1341 (2009)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    B. Bao, H. Bao, N. Wang, M. Chen, Q. Xu, Chaos Solitons Fractals 94, 102 (2017)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    V.-T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, X. Wang, A chaotic hyperjerk system based on memristive device, in Advances and Applications in Chaotic Systems (Springer International Publishing, 2016), pp. 39–58Google Scholar
  31. 31.
    K. Rajagopal, H. Jahanshahi, M. Varan, I. Bayr, V.-T. Pham, S. Jafari, A. Karthikeyan, A.E.U. Int, J. Electron. Commun. 94, 55 (2018)CrossRefGoogle Scholar
  32. 32.
    A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)CrossRefGoogle Scholar
  33. 33.
    J.L. Hindmarsh, R. Rose, Proc. R. Soc. London B 221, 87 (1984)ADSCrossRefGoogle Scholar
  34. 34.
    M. Lv, C. Wang, G. Ren, J. Ma, X. Song, Nonlinear Dyn. 85, 1479 (2016)CrossRefGoogle Scholar
  35. 35.
    B. Bao, A. Hu, H. Bao, Q. Xu, M. Chen, H. Wu, Complexity 2018, 3872573 (2018)Google Scholar
  36. 36.
    E.R. Kandel, J.H. Schwartz, T.M. Jessell, S.A. Siegelbaum, A.J. Hudspeth, in Principles of neural science ((McGraw-hill, New York, 2000), Vol. 4Google Scholar
  37. 37.
    V. Resmi, G. Ambika, R. Amritkar, Phys. Rev. E 84, 046212 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    S. Majhi, M. Perc, D. Ghosh, Chaos: Interdiscip. J. Nonlinear Sci. 27, 073109 (2017)CrossRefGoogle Scholar
  39. 39.
    Z. Faghani, Z. Arab, F. Parastesh, S. Jafari, M. Perc, M. Slavinec, Chaos Solitons Fractals 114, 306 (2018)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    F. Parastesh, S. Jafari, H. Azarnoush, B. Hatef, A. Bountis, Chaos Solitons Fractals 110, 203 (2018)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    P. Jaros, Y. Maistrenko, T. Kapitaniak, Phys. Rev. E 91, 022907 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    T. Kapitaniak, P. Kuzma, J. Wojewoda, K. Czolczynski, Y. Maistrenko, Sci. Rep. 4, 6379 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    Y. Maistrenko, S. Brezetsky, P. Jaros, R. Levchenko, T. Kapitaniak, Phys. Rev. E 95, 010203 (2017)ADSCrossRefGoogle Scholar
  44. 44.
    Z. Rostami, V.T. Pham, S. Jafari, F. Hadaeghi, J. Ma, Appl. Math. Comput. 338, 141 (2018)MathSciNetGoogle Scholar
  45. 45.
    Z. Rostami, K. Rajagopal, A.J.M. Khalaf, S. Jafari, M. Perc, M. Slavinec, Physica A 509, 1162 (2018)ADSCrossRefGoogle Scholar
  46. 46.
    B. Bao, Z. Liu, J. Xu, Electron. Lett. 46, 237 (2010)Google Scholar
  47. 47.
    B. Muthuswamy, Int. J. Bifurc. Chaos 20, 1335 (2010)CrossRefGoogle Scholar
  48. 48.
    M. Lv, C. Wang, G. Ren, J. Ma, X. Song, Nonlinear Dyn. 85, 1 (2016)CrossRefGoogle Scholar
  49. 49.
    Q. Li, H. Zeng, J. Li, Nonlinear Dyn. 79, 2295 (2015)CrossRefGoogle Scholar
  50. 50.
    S. Panahi, S. Jafari, A.J.M. Khalaf, K. Rajagopal, V.T. Pham, F.E. Alsaadi, Chin. J. Phys. 56, 2254 (2018)CrossRefGoogle Scholar
  51. 51.
    V. Dakos, S.M. Glaser, C.-H. Hsieh, G. Sugihara, J. Royal Soc. Interf. 14, 20160845 (2017)CrossRefGoogle Scholar
  52. 52.
    V. Dakos, F. Soler-Toscano, Ecol. Complexity 32, 144 (2017)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yongjian Liu
    • 1
  • Fahimeh Nazarimehr
    • 2
    Email author
  • Abdul Jalil M. Khalaf
    • 3
  • Ahmed Alsaedi
    • 4
  • Tasawar Hayat
    • 4
    • 5
  1. 1.Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal UniversityYulin, GuangxiP.R. China
  2. 2.Biomedical Engineering Department, Amirkabir University of TechnologyTehranIran
  3. 3.Ministry of Higher Education and Scientific ResearchBaghdadIraq
  4. 4.NAAM Research Group, King Abdulaziz, University of JeddahJeddahSaudi Arabia
  5. 5.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan

Personalised recommendations