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An adaptive synchronization approach in a network composed of four neurons with energy diversity

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Abstract

Due to the diversity in excitability and some intrinsic parameters, these neurons present different firing patterns and energy diversity becomes distinct. As a result, flexible synapses are guided to connect neurons clustered in the same region for generating fast synchronous firing patterns, and then energy balance is stabilized between neurons. In this work, four FitzHugh–Nagumo (FHN) neurons in chain network and ring network are connected via memristive synapses, and the collective neural activities are controlled by taming the memristive coupling adaptively via Heaviside function, which the coupling intensity is increased exponentially to reaches a saturation value under complete synchronization and energy balance between neurons. Bifurcation analysis, Lyapunov exponent spectrum and Hamilton energy for single neuron are calculated to find dynamics dependence on external stimulus and parameters. The Heaviside function terminates the increase in coupling intensity when energy diversity between adjacent neurons is decreased to a tiny value, which means reaching local energy balance in the neural network. The error function, phase error and energy error are used to explore the collective behaviors of network during the adaptive energy propagation. It is found that identical neurons can reach complete synchronization and energy balance well while the nonidentical neurons can reach phase lock and firing patterns become unstable even under energy balance. This discussion provides a clue to understand the biophysical mechanism for control of synapse growth in the network under energy flow, and external energy injection can be effective to control the neural networks.

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References

  1. E M Izhikevich Int J Bifurcat Chaos. 10 1171 (2000)

    Article  MathSciNet  Google Scholar 

  2. S Zhang, J Zheng, X Wang and Z Zeng Chaos Solitons & Fractals 145 110761 (2021)

    Article  Google Scholar 

  3. S Zhang, J Zheng, X Wang and Z Zeng Chaos 31 011101 (2021)

    Article  ADS  Google Scholar 

  4. E B M Ngouonkadi, H B Fotsin, P L Fotso and V K H C TambaCerdeira Solitons & Fractals 85 151 (2016)

    Article  ADS  Google Scholar 

  5. Y Liu, W Xu, J Ma, F Alzahrani and A Hobiny Front. Inform. Technol. Electron. 21 1387 (2020)

    Article  Google Scholar 

  6. Y Xu, Y Guo, G Ren and J Ma Appl. Math. Comput. 385 125427 (2020)

    MathSciNet  Google Scholar 

  7. Y Guo, P Zhou, Z Yao and J Ma Nonlinear Dyn. 105 3603 (2021)

    Article  Google Scholar 

  8. F Wu, Y Guo and J Ma Nonlinear Dyn. 109 2063 (2022)

    Article  Google Scholar 

  9. Z Liu, P Zhou, J Ma, A Hobiny and F Alzahrani Chaos Solitons & Fractals 131 109533 (2020)

    Article  MathSciNet  Google Scholar 

  10. C Liu, J Wang, H Yu, B Deng, X L We, K M Tsang and W Chan Chaos 23 033121 (2013)

    Article  ADS  Google Scholar 

  11. H Yu, J Wang, C Liu, B Deng and X Wei Physica A 392 5473 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  12. F Wu, X Hu and J Ma Appl. Math. Comput. 432 127366 (2022)

    Google Scholar 

  13. H Bao, W Liu and A Hu Nonlinear Dyn. 95 43 (2019)

    Article  Google Scholar 

  14. Z T Njitacke, J Awrejcewicz, A N K Telem, T F Fozin and J Kengne IEEE Tr Circ. Syst. II: Express Briefs (2022). https://doi.org/10.1109/TCSII.2022.3172141

    Article  Google Scholar 

  15. T Z Njitacke, M S Shankar, F T Fonzin, G D Leutcho and J Awrejcewicz Chaos 32 053114 (2022)

    Article  ADS  Google Scholar 

  16. Y Zhang, C N Wang, J Tang and J Ma Sci China Technol. Sci. 63 2328 (2020)

    Article  ADS  Google Scholar 

  17. J T Fossi, V Deli, H C Edima, Z T Njitacke, F F Kemwoue and J Atangana Euro Phys. J. B 95 66 (2022)

    Article  ADS  Google Scholar 

  18. F Xu, J Zhang, T Fang, S Huang and M Wang Nonlinear Dyn. 92 1395 (2018)

    Article  Google Scholar 

  19. Y Guo, Z Zhu, C Wang and G Ren Optik 218 164993 (2020)

    Article  ADS  Google Scholar 

  20. F Meng, X Zeng and Z Wang Nonlinear Dyn. 95 1615 (2019)

    Article  Google Scholar 

  21. S Rakshit, A Ray and B K D BeraGhosh Nonlinear Dyn. 94 785 (2018)

    Article  Google Scholar 

  22. P Zhou, Z Yao, J Ma and Z Zhu Chaos Solitons & Fractals 145 110751 (2021)

    Article  Google Scholar 

  23. F Parastesh, H Azarnoush, S Jafari, B Hatef, M Perc and R Repnik Appl Math. Comput. 350 217 (2019)

    MathSciNet  Google Scholar 

  24. A Mondal, S K Sharma, R K Upadhyay and A Mondal Sci Rep. 9 15721 (2019)

    Article  ADS  Google Scholar 

  25. S Mostaghimi, F Nazarimehr, S Jafari and J Ma Appl Math. Comput. 348 42 (2019)

    MathSciNet  Google Scholar 

  26. Y Xu and J Ma Commun. Nonlinear Sci. Numer. Simulat. 111 106426 (2022)

    Article  Google Scholar 

  27. C N Takembo, P Nyifeh, H P E Fouda and T C Kofane Physica A 593 126891 (2022)

    Article  Google Scholar 

  28. I Hussain, S Jafari, D Ghosh and M Perc Nonlinear Dyn. 104 2711 (2021)

    Article  Google Scholar 

  29. Y Liu, Y Xu and J Ma Commun Nonlinear Sci. Numer. Simulat. 89 105297 (2020)

    Article  Google Scholar 

  30. M M Ibrahim, M A Kamran, M M N Mannan, I L H Jung and S Kim Sci Rep 11 3884 (2021)

    Article  ADS  Google Scholar 

  31. L Qu, L Du, Z Cao, H Hu and Z Deng Solitons & Fractals 144 110646 (2021)

    Article  Google Scholar 

  32. Z T Njitacke, C N Takembo, J Awrejcewicz, H P Ekobena Fouda and J Kengne Chaos Solitons & Fractals 160 112211 (2022)

    Article  Google Scholar 

  33. T Y Li, G W Wang, D Yu, Q M Ding and Y Jia Nonlinear Dyn. 108 2611 (2022)

    Article  Google Scholar 

  34. H Bao, Y Zhang, W B Liu and B C Bao Nonlinear Dyn. 100 937 (2020)

    Article  Google Scholar 

  35. C N Takembo, H P E Fouda and T C Kofane Indian J Phys (2022). https://doi.org/10.1007/s12648-022-02368-2

    Article  Google Scholar 

  36. A S Tankou Tagne, C N Takembo, H G Ben-Bolie and P Owona Ateba PLOS one 14 6 e0214989 (2019). https://doi.org/10.1371/journal.pone.0214989

    Article  Google Scholar 

  37. X Sun and T Xue Int. J. Bifurcat. Chaos 28 1850143 (2018)

    Article  Google Scholar 

  38. F Su, J Wang, H Li, X Wei, H Yu and B Deng Commun. Nonlinear Sci. Numer. Simulat. 55 29 (2018)

    Article  ADS  Google Scholar 

  39. C N Takembo Mod Phys Lett B 36 2250021 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  40. Z Yao and C Wang Chaos Solitons & Fractals 152 111361 (2021)

    Article  Google Scholar 

  41. E V Rybalova, A Zakharova and G I Strelkova Chaos Solitons & Fractals 148 111011 (2021)

    Article  Google Scholar 

  42. G Wang, L Yang, X Zhan, A Li and Y Jia Nonlinear Dyn. 107 3945 (2022)

    Article  Google Scholar 

  43. C N Takembo, A Mvogo, H P Ekobena Fouda and T Crépin Kofané Nonlinear Dyn. 95 1067 (2019)

    Article  Google Scholar 

  44. J Zhao, Y Qin, Y Che and H J RanLi Cogn Neurodyn. 14 399 (2020)

    Article  Google Scholar 

  45. E Baspinar, L Schülen and S A OlmiZakharova Phys Rev. E 103 032308 (2021)

    Article  ADS  Google Scholar 

  46. R FitzHugh Bull. Math. Biophys. 17 257 (1955)

    Article  Google Scholar 

  47. J Nagumo, S Arimoto and S Yoshizawa Proc IRE 50 2061 (1962)

    Article  Google Scholar 

  48. I M Kyprianidis, V Papachristou, I N Stouboulos and C Volos WSEAS Trans Syst. 11 516 (2012)

    Google Scholar 

  49. R FitzHugh Biophys J. 1 445 (1961)

    Article  ADS  Google Scholar 

  50. K Li, H Bao, H Li, J Ma, Z Y Hua and B C Bao IEEE Tran Industrial Infor. 18 1726 (2021)

    Article  Google Scholar 

  51. B C Bao, Y X Zhu, J Ma, H Bao and H G Wu Sci China Technol. Sci. 64 1107 (2021)

    Article  ADS  Google Scholar 

  52. C Li, Y Yang, J Du and Z Chen Euro Phys. J. Special Topics 230 1723 (2021)

    Article  ADS  Google Scholar 

  53. N Raj, R K Ranjan and F Khateb IEEE Tr. Very Large Scale Integrat. (VLSI) Syst. 28 1050 (2020). https://doi.org/10.1109/TVLSI.2020.2966292

    Article  Google Scholar 

  54. S S Sajjadi, D Baleanu, A Jajarmi and H M Pirouz Chaos Solitons & Fractals 138 109919 (2020)

    Article  MathSciNet  Google Scholar 

  55. H Salarieh and M Shahrokhi Chaos Solitons & Fractals 37 125 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  56. Y Yu Chaos Solitons & Fractals 36 329 (2008)

    Article  ADS  Google Scholar 

  57. J Ma, A H Zhang, Y F Xia and L P Zhang Appl. Math. Comput. 215 3318 (2010). https://doi.org/10.1016/j.amc.2009.10.020

    Article  MathSciNet  Google Scholar 

  58. Z Zhang, X Wang and Z Du Appli Math. Comput. 218 6833 (2012)

    Article  Google Scholar 

  59. X F Zhang and J Ma J Zhejiang Univ-Sci A (Appl Phys Eng) 22 707 (2021)

    Article  Google Scholar 

  60. D Yu, G W Wang, T Y Li and Q M Y DingJia Commun Nonlin. Sci. Numer. Simulat. 117 106894 (2023)

    Article  Google Scholar 

  61. Y Xie, P Zhou, Z Yao and J Ma Physica A 607 128175 (2022)

    Article  Google Scholar 

  62. Y Xie and J Ma J. Biol. Phys. 48 339 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

This project is partially supported by the National Science Foundation of China under grant No.12062009.

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Feifei Yang & Jun Ma

  2. School of Physics and Information Technology, Shaanxi Normal University, Xi′an, 710062, China

    Ya Wang

  3. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jun Ma

Authors
  1. Feifei Yang
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  2. Ya Wang
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  3. Jun Ma
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Contributions

Feifei Yang and Ya Wang finished the numerical calculation and wrote the original draft. Jun Ma designed the research and wrote final version.

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Correspondence to Jun Ma.

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Yang, F., Wang, Y. & Ma, J. An adaptive synchronization approach in a network composed of four neurons with energy diversity. Indian J Phys 97, 2125–2137 (2023). https://doi.org/10.1007/s12648-022-02562-2

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