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Hamilton energy dependence and quasi-synchronization behaviors of non-identical dynamic systems

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Abstract

It becomes crucial to calculate the Hamilton energy and its evolution when exploring dynamics characters in nonlinear systems. Based on the Helmholtz’s theorem, the Hamilton energy of the HR system in an electric field and the modified Chua’s circuit are calculated and analyzed. Then the energy feedback is used to control the system to the desired states. The results show that this method can not only effectively suppress the chaotic behavior of the system, but also induce abundant discharge behavior. In addition, the synchronization behavior of the two HR systems or Chua’s circuits is explored respectively using the adaptive synchronization control method. Taking into account that different Lyapunov functions will yield different results, we propose the idea that the coefficient ratio of each state variable in the Hamilton energy function can be utilized to design the Lyapunov function for the dynamic systems in this paper. It is found that the controller and parameter adaptive law obtained by this method can make the drive system and response system realize quasi-synchronization. This result provides an effective method for further exploring adaptive synchronization between neurons.

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References

  1. A Akgul, H Calgan and I Koyuncu I Pehlivan and A Istanbullu Nonlinear Dynamics. 84 481 (2016)

    Article  Google Scholar 

  2. V Pham and J Sajad X Wang and J Ma International Journal of Bifurcation. 26 1650069 (2016)

    ADS  Google Scholar 

  3. X L An and L Zhang Nonlinear Dynamics. 94 2995 (2018)

    Article  Google Scholar 

  4. W M Ahmad and J C Sprott Solitons and Fractals. 16 339 (2003)

    Article  ADS  Google Scholar 

  5. U E Kocamaz Systems & Computers. 27 1850057 (2018)

    Google Scholar 

  6. X L An, L Xiong and Q Q Shi S Qiao and L Zhang Nonlinear Dynamics. 111 9509 (2023)

    Article  Google Scholar 

  7. C N Wang R T Chu and J Ma Complexity. 21 370 (2015)

    Google Scholar 

  8. S Vaidyanathan Archives of Control Sciences. 26 19 (2016)

  9. G Zhang, J Ma and A Alsaedi B Ahmad and F Alzahrani Applied Mathematics & Computation. 321 290 (2018)

    Google Scholar 

  10. Z Yao and P Zhou Z G Zhu and J Ma Neurocomputing. 423 518 (2021)

    Article  Google Scholar 

  11. S L Guo J Ma and A Alsaedi Pramana: Journal of Physics. 90 267 (2018)

    Google Scholar 

  12. B Du Y R Liu and I A Abbas Journal of the Franklin Institute. 353 448 (2016)

    Article  Google Scholar 

  13. L Chua Circuit Theory. 18 507 (1971)

  14. Q Xu, S Cheng and Z T Ju M Chen and H G Wu Chinese Journal of Physics. 70 69 (2021)

    ADS  Google Scholar 

  15. X Zhang, C B Li and Y D Chen Solitons & Fractals. 139 110000 (2020)

    Article  Google Scholar 

  16. Y T Guo and Z Yao Y Xu and J Ma International Journal of Electronics & Communications. 145 154074 (2022)

    Google Scholar 

  17. X F Zhang, F Q Wu, J Ma and A Hobiny F Alzahrani and G D Ren International Journal of Electronics & Communications. 115 153050 (2020)

    Google Scholar 

  18. X L An and S Qiao Solitons and Fractals 143 110587 (2021)

    Article  Google Scholar 

  19. X W Ma and Y Xu Solitons & Fractals. 159 112149 (2022)

    Article  Google Scholar 

  20. X L An, L Xiong and L Zhang J G Zhang and Q Q Shi The European Physical Journal Plus. 137 1362 (2022)

    Article  ADS  Google Scholar 

  21. B Mireille J. M Pierre Cell Metabolism. 14 724 (2011)

    Article  Google Scholar 

  22. L L Lu, Y Jia, Y Xu and M Y Ge L J Yang and X Zhan Science China Technological Sciences. 62 427 (2019)

    Article  ADS  Google Scholar 

  23. C N Wang Y Wang and J Ma Acta Physica Sinica. 65 240501 (2016)

    Article  ADS  Google Scholar 

  24. F Q Wu and T Hayat X L An and J Ma Nonlinear Dynamics. 94 669 (2018)

    Article  Google Scholar 

  25. P Zhou and X K Hu Solitons & Fractals. 150 111154 (2021)

    Article  Google Scholar 

  26. C Sarasola, F J Torrealdea, A d’Anjou, A Moujahid and M Graña Physical Review. E. 69 011606 (2004)

  27. J Ma, F Q Wu and W Y Jin P Zhou and T Hayat Chaos: An Interdisciplinary Journal of Nonlinear Science. 27 053108 (2017)

    Google Scholar 

  28. K Usha and P A Subha Chinese Physics B. 28 020502 (2019)

    Article  ADS  Google Scholar 

  29. X L An and S Qiao Acta Physica Sinica. 70 050501 (2021)

    Article  Google Scholar 

  30. F J Torrealdea Solitons and Fractals. 40 60 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  31. M Grana and A d’Anjou F J Torrealdea and C Sarasola Physical Review E. 74 011905 (2006)

    Article  ADS  Google Scholar 

  32. J Ma Chaos Theory and Applications. 4 1 (2022)

  33. A I Khibnik D Roose and L O Chua International Journal of Bifurcation and Chaos. 3 363 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  34. G Q Zhong IEEE Transactions on Circuits & Systems. 41 934 (1994)

  35. X L Song W Y Jin and J Ma Chinese Physics B. 24 128710 (2015)

    Article  ADS  Google Scholar 

  36. Y R Liu and W B Liu M A Obaid and I A Abbas Neurocomputing. 177 409 (2016)

    Google Scholar 

  37. D Liu, Z D Wang and Y R Liu C F Xue and F E Alsaadi Applied Mathematics and Computation. 440 127669 (2023)

    Google Scholar 

  38. B Z Liu and J H Peng Nonlinear dynamics (Bei Jing: Chinese High Education Press). 26 (2004)

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Acknowledgements

This work is supported by the National Natural Science Foundation (No. 11962012), the key project of the Gansu Province Natural Science Foundation of China (No. 23JRRA861), and the Youth Science and Technology Innovation Project of Lanzhou Institute of Technology (No. 2021KJ-08).

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Authors and Affiliations

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Lingfeng Jiang & Xinlei An

  2. The Basic Courses Department of Lanzhou Institute of Technology, Lanzhou, 730050, China

    Li Zhang

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  1. Lingfeng Jiang
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Correspondence to Xinlei An.

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Jiang, L., Zhang, L. & An, X. Hamilton energy dependence and quasi-synchronization behaviors of non-identical dynamic systems. Indian J Phys 98, 2873–2890 (2024). https://doi.org/10.1007/s12648-023-03061-8

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