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Suppression of chaos via control of energy flow

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Abstract

Continuous energy supply is critical and important to support oscillating behaviour; otherwise, the oscillator will die. For nonlinear and chaotic circuits, enough energy supply is also important to keep electric devices working. In this paper, Hamilton energy is calculated for dimensionless dynamical system (e.g., the chaotic Lorenz system) using Helmholtz’s theorem. The Hamilton energy is considered as a new variable and then the dynamical system is controlled by using the scheme of energy feedback. It is found that chaos can be suppressed even when intermittent feedback scheme is applied. This scheme is effective to control chaos and to stabilise other dynamical systems.

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References

  1. M Sirshendu, M Achintya and S Swarnendu, Pramana – J. Phys. 84, 443 (2015)

    Article  Google Scholar 

  2. R Pool, Science 243(4891), 604 (1989)

    Article  ADS  Google Scholar 

  3. L W Zhao and J L Yin, Pramana – J. Phys. 87, 2 (2016)

    Article  Google Scholar 

  4. C G Langton, Physica D 42, 12 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  5. V Madhok, C A Riofrio and I H Deutsch, Pramana – J. Phys. 87, 65 (2016)

    Article  ADS  Google Scholar 

  6. T Sugawara, M Tachikawa, T Tsukamoto and T Shimizu, Phys. Rev. Lett. 72, 3502 (1994)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. S Boccaletti et al, Phys. Rep. 329, 103 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  9. S Boccaletti et al, Phys. Rep. 366, 1 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  10. M Feki, Chaos Solitons Fractals 18, 141 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  11. B Moghaddam, Neuron 40, 881 (2003)

    Article  Google Scholar 

  12. C G Li and G R Chen, Chaos Solitons Fractals 22, 549 (2004)

    Article  ADS  Google Scholar 

  13. D B Xiu and G E Karniadakis, SIAM J. Sci. Comput. 24, 619 (2006)

    Article  Google Scholar 

  14. S Dadras, H R Momeni and G Y Qi, Nonlinear Dyn. 62, 391 (2010)

    Article  Google Scholar 

  15. C N Wang et al, Nonlinear Dyn. 67, 139 (2012)

    Article  Google Scholar 

  16. S M Huan, Q D Li and X S Yang, Nonlinear Dyn. 69, 1915 (2012)

    Article  Google Scholar 

  17. X Wang, P Viet-Thanh and C Volos, Complexity 2017, 7138971 (2017)

    Google Scholar 

  18. C N Wang et al, Complexity 21, 370 (2015)

    Article  MathSciNet  Google Scholar 

  19. L H Yuan, C N Wang and Z Z Zhang, Indian J. Phys. 90, 1155 (2016)

    Article  ADS  Google Scholar 

  20. J Ma et al, Appl. Math. Comput. 298, 65 (2017)

    MathSciNet  Google Scholar 

  21. J Kengne, A N Negou and D Tchiotsop, Nonlinear Dyn. 88, 2589 (2017)

    Article  Google Scholar 

  22. S Sabarathinam, C K Volos and K Thamilmaran, Nonlinear Dyn. 87, 37 (2017)

    Article  Google Scholar 

  23. P Viet-Thanh et al, Int. J. Bifurc. Chaos 26, 1650069 (2016)

    Article  Google Scholar 

  24. J Ma et al, Nonlinear Dyn. 76, 1951 (2014)

    Article  Google Scholar 

  25. X Y Wu et al, Nonlinear Dyn. 75, 113 (2014)

    Article  Google Scholar 

  26. X Y Hu et al, Nonlinear Dyn. 86, 1725 (2016)

    Article  Google Scholar 

  27. G D Ren, Y Xu and C N Wang, Nonlinear Dyn. 88, 893 (2017)

    Article  Google Scholar 

  28. J Ma et al, Neurocomput. 167, 378 (2015)

    Article  Google Scholar 

  29. J Tang et al, Phys. Rev. E 88, 032906 (2013)

    Article  ADS  Google Scholar 

  30. G D Ren et al, Commun. Nonlinear Sci. Numer. Simulat. 29, 170 (2015)

    Article  Google Scholar 

  31. M Ochowski, Physica D 145, 181 (2000)

    Article  ADS  Google Scholar 

  32. C Sarasola et al, Phys. Rev. E 69, 011606 (2004)

    Article  ADS  Google Scholar 

  33. C N Wang, Y Wang and J Ma, Acta Phys. Sin. 65, 240501 (2016)

    Google Scholar 

  34. D H Kobe, Am. J. Phys. 54(6), 552 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  35. L G de la Fraga and E Tlelo-Cuautle, Nonlinear Dyn. 76, 1503 (2014)

    Article  Google Scholar 

  36. A Wolf et al, Physica D 16, 285 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  37. X S Luo, Acta Phys. Sin. 48, 402 (1999)

    Google Scholar 

  38. X Zhang and K Shen, Phys. Rev. E 63, 046212 (2001)

    Article  ADS  Google Scholar 

  39. X D Jing and L Lv, Acta Phys. Sin. 57, 4766 (2008)

    Google Scholar 

  40. J Ma et al, Chin. Phys. Lett. 25, 3582 (2008)

    Article  ADS  Google Scholar 

  41. W Y Jin et al, Complexity 2017, 4797545 (2017)

  42. Y Wang and J Ma, Optik  139, 231 (2017)

    Article  ADS  Google Scholar 

  43. L L Lu et al, Complexity 2017, 7628537 (2017)

    Google Scholar 

  44. F Q Wu et al, Physica A 469, 81 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  45. Y Wang et al, Int. J. Bifurc. Chaos 27, 1750030 (2017)

    Article  Google Scholar 

  46. J Ma, F Q Wu and C N Wang, Int. J. Phys. B 31, 1650251 (2017)

    Article  ADS  Google Scholar 

  47. J Ma et al, Appl. Math. Comput. 307, 321 (2017)

    MathSciNet  Google Scholar 

  48. N Cai, C Diao and M J Khan, Complexity 2017, 4978613 (2017)

    Article  Google Scholar 

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Acknowledgements

This work is partially supported by National Natural Science Foundation of China under Grant No. 11372122.

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Authors and Affiliations

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

    Shengli Guo & Jun Ma

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

    Jun Ma

  3. NAAM-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Ahmed Alsaedi

Authors
  1. Shengli Guo
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  2. Jun Ma
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  3. Ahmed Alsaedi
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Correspondence to Jun Ma.

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Guo, S., Ma, J. & Alsaedi, A. Suppression of chaos via control of energy flow. Pramana - J Phys 90, 39 (2018). https://doi.org/10.1007/s12043-018-1534-0

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  • DOI: https://doi.org/10.1007/s12043-018-1534-0

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