Advertisement

Pramana

, 90:54 | Cite as

Control and synchronisation of a novel seven-dimensional hyperchaotic system with active control

  • Metin Varan
  • Akif Akgul
Article
  • 136 Downloads

Abstract

In this work, active control method is proposed for controlling and synchronising seven-dimensional (7D) hyperchaotic systems. The seven-dimensional hyperchaotic system is considered for the implementation. Seven-dimensional hyperchaotic system is also investigated via time series, phase portraits and bifurcation diagrams. For understanding the impact of active controllers on global asymptotic stability of synchronisation and control errors, the Lyapunov function is used. Numerical analysis is done to reveal the effectiveness of applied active control method and the results are discussed.

Keywords

Chaos control chaos synchronisation active control seven-dimensional hyperchaotic system 

PACS No

05.45 

References

  1. 1.
    R Trejo-Guerra, E Tlelo-Cuautle, V H Carbajal-Gomez and G Rodriguez-Gomez, Appl. Math. Comput. 219(10), 5113 (2013)MathSciNetGoogle Scholar
  2. 2.
    R Trejo-Guerra, E Tlelo-Cuautle, J M Jimnez-Fuentes, C Snchez-Lpez, J M Muoz-Pacheco, G Espinosa-Flores-Verdad and J M Rocha-Prez, Commun. Nonlinear Sci. Numer. Simulat. 17(11), 4328 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    X Wang, V T Pham, S Jafari, C Volos, J M Munoz-Pacheco and E Tlelo-Cuautle, IEEE Access 5, 8851 (2017)CrossRefGoogle Scholar
  4. 4.
    J L Valtierra-Sanchez, E Tlelo-Cuautle and A R-Vázquez, Int. J. Circuit Theory Appl. 45(2), 305 (2017)CrossRefGoogle Scholar
  5. 5.
    J C Nez, E Tlelo, C Ramirez and J M Jimenez, IEEE Latin America Trans. 13(9), 2865 (2015)CrossRefGoogle Scholar
  6. 6.
    J M Munoz-Pacheco, E Tlelo-Cuautle, I Toxqui-Toxqui, C Sanchez-Lopez and R Trejo-Guerra, Int. J. Electron. 101(11), 1559 (2014)CrossRefGoogle Scholar
  7. 7.
    E Tlelo-Cuautle, H C Ramos-Lopez, M Sanchez-Sanchez, A D Pano-Azucena, L A Sanchez-Gaspariano, J C Nuez-Perez and J L Camas-Anzueto, J. Elec. Engng - Elektrotechnick Casopis 65(3), 157 (2014)Google Scholar
  8. 8.
    R Trejo-Guerra, E Tlelo-Cuautle, J M Jiménez-Fuentes, J M Muñoz-Pacheco, C Snchez-Lpez and R Trejo-Guerra, Int. J. Circuit Theory Appl. 41(8), 831 (2013)CrossRefGoogle Scholar
  9. 9.
    Y Line, C Wang, H He and L L Zhou, Pramana –Phys. 86(4), 801 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    C Li and Y Tong, Pramana – J. Phys. 80(4), 583 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    O E Rossler, Phys. Lett. A 71, 155 (1979)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    K Thamilmaran, M Lakshmanan and V Venkatesan, Int. J. Bifurc. Chaos 14, 221 (2004)CrossRefGoogle Scholar
  13. 13.
    R Barboza, Int. J. Bifurc. Chaos 18, 1151 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Q A Jia, Phys. Lett. A 366(3), 217 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    X Wei, L Guo, Q Zhang, J Zhang and S Lian, J. Syst. Softw. 85, 290 (2012)CrossRefGoogle Scholar
  16. 16.
    H Y Jia, Z Q Chen and Z Z Yuan, Chin. Phys. B 19(2), 020507 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Y Zeng, Comput. Engng Manage. Sci. 2, 385 (2011)Google Scholar
  18. 18.
    S Vaidyanathan, C K Volos and V T Pham, J. Engng Sci. Techn. Rev. 8(2), 232 (2015)Google Scholar
  19. 19.
    G Y Qi, M A van Wyk, B J van Wyk and G R Chen, Phys. Lett. A 372(2), 124 (2008)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    G Kai, W Zhang, Z C Wei, J F Wang and A Akgul, Mathematical Problems in Engineering, 2490580 (2017).Google Scholar
  21. 21.
    Z Wei, I Moroz, J C Sprott, A Akgul and W Zhang, Chaos 27(3), 033101 (2017)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    S Vaidyanathan, V T Pham and C K Volos, Eur. Phys. J. Special Topics 224(8), 1575 (2015).ADSCrossRefGoogle Scholar
  23. 23.
    Q Yang and C Chen, Int. J. Bifurc. Chaos 23(6), 1350109 (2013)CrossRefGoogle Scholar
  24. 24.
    X Wu, D Wang, J Kurths and H Kan, Inform. Sci. 349, 137 (2016)CrossRefGoogle Scholar
  25. 25.
    D Z Liu, J L Zhu and H Sun, Int. J. Control Automation 7(4), 385 (2014)CrossRefGoogle Scholar
  26. 26.
    M Krstic, I Kanellakopoulos and P V Kokotovic, Nonlinear adaptive control design (Wiley, 1995)Google Scholar
  27. 27.
    V I Utkin, IEEE Trans. Ind. Electron. 40(1), 23 (1993)CrossRefGoogle Scholar
  28. 28.
    U E Kocamaz and Y Uyaroglu, Nonlinear Dynam. 75(1–2), 63 (2014)MathSciNetCrossRefGoogle Scholar
  29. 29.
    J Hu, L Liu and D W Ma, J. Korean Phys. Soc. 65(12), 2132 (2014)ADSCrossRefGoogle Scholar
  30. 30.
    R Rakkiyappan, R Sivasamy and J H Park, Can. J. Phys. Can. 92(12), 1688 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    W Yu, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 46(7), 876 (1999)Google Scholar
  32. 32.
    D L Qi, G Z Zhao and Y Z Song, 5th World Congress on Intelligent Control and Automation (Hangzhou, 2004) Vol. 2, p. 1284Google Scholar
  33. 33.
    B T Cui and M G Hua, Chaos Solitons Fractals 29(2), 331 (2006)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    F Wang and C Liu, Physica D 225(1), 55 (2007)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    X R Chen and C X Liu, Nonlinear Anal.: Real World Appl. 11(2), 683 (2010)Google Scholar
  36. 36.
    O Marquet, D Sipp and L Jacquin, J. Fluid Mech. 615, 221 (2008)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Y Uyaroglu and S Emiroglu, J. Vib. Control 21(8), 1657 (2015)MathSciNetCrossRefGoogle Scholar
  38. 38.
    F Q Wang and C X Liu, Physica D 225(1), 55 (2007)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    D Zhao and A S Morgans, J. Sound Vib. 320(4), 744 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    U E Kocamaz, A Goksu, H Taskin and Y Uyaroglu, Inf. Technol. Control 44(2), 172 (2015)Google Scholar
  41. 41.
    W Xiang-Jun, L Jing-Sen and C Guan-Rong, Nonlinear Dynam. 53(1–2), 45 (2008)MathSciNetCrossRefGoogle Scholar
  42. 42.
    M A Franchek, M W Ryan and R J Bernhard, J. Sound Vib. 189(5), 565 (1996)ADSCrossRefGoogle Scholar
  43. 43.
    R Rakkiyappan, R Sivasamy and X D Li, Circuits Syst. Signal Process. 34(3), 763 (2015)CrossRefGoogle Scholar
  44. 44.
    H L Li, Y L Jiang and Z L Wang, Nonlinear Dynam. 79(2), 919 (2015)MathSciNetCrossRefGoogle Scholar
  45. 45.
    T L Carroll and L M Pecora, IEEE Trans. Circuits Systems 38(4), 453 (1991)CrossRefGoogle Scholar
  46. 46.
    K Ojo, S T Ogunjo and O Williams, Cybern. Phys. 2(1), 31 (2013)Google Scholar
  47. 47.
    K Kemih, H Bouraoui, M Messadi and M Ghanes, Acta Phys. Polon. A 123(2), 193 (2013)CrossRefGoogle Scholar
  48. 48.
    S Vaidyanathan, C Volos and V T Pham, Arch. Control Sci. 24(4), 409 (2014)MathSciNetGoogle Scholar
  49. 49.
    Y Lu, P He, S Ma, G Z Li and S Mobayben, Pramana – J. Phys. 86(6), 1413 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    Y Feng and W Q Pan, Pramana – J. Phys. 88(62), 1 (2017)Google Scholar
  51. 51.
    E Tlelo-Cuautle, L G de la Fraga and J R Magdaleno, Chaotic systems, artificial neural networks, random number generators, and secure communication systems (Springer, 2016)Google Scholar
  52. 52.
    T E Cuautle, Q V AdJ, L G Fraga, Rangel-Magdaleno JdJ, PLoS ONE 11(12), 1 (2016)Google Scholar
  53. 53.
    E Tlelo-Cuautle, L G de la Fraga, V T Pham, C Volos, S Jafari and A J Quintas-Valles, Nonlinear Dynam. 89(2), 1129 (2017)CrossRefGoogle Scholar
  54. 54.
    E Tlelo-Cuautle, A D Pano-Azucena, J J Rangel-Magdaleno, V H Carbajal-Gomez and G Rodriguez-Gomez, Nonlinear Dynam. 85(4), 2143 (2016)CrossRefGoogle Scholar
  55. 55.
    E. Tlelo-Cuautle, V H Carbajal-Gomez, P J Obeso-Rodelo, J J Rangel-Magdaleno and J C Nez-Prez, Nonlinear Dynam82(4), 1879 (2015)MathSciNetCrossRefGoogle Scholar
  56. 56.
    E Tlelo-Cuautle, J J Rangel-Magdaleno, A D Pano-Azucena, P J Obeso-Rodelo and J C Nuez-Perez, Commun. Nonlinear Sci. Numer. Simul. 27(1–3), 66 (2015)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    L G de la Fraga and E Tlelo-Cuautle, Nonlinear Dynam. 76(2), 1503 (2014)CrossRefGoogle Scholar
  58. 58.
    V H Carbajal-Gomez, E Tlelo-Cuautle, F V Fernández, L G de la Fraga and C Sánchez-López, Int. J. Nonlinear Sci. Numer. Simul. 15(1), 11 (2014)MathSciNetCrossRefGoogle Scholar
  59. 59.
    V H Carbajal-Gómez, E Tlelo-Cuautle and F V Fernández, Appl. Math. Comput. 219(15), 8163 (2013)MathSciNetGoogle Scholar
  60. 60.
    E Tlelo-Cuautle, V H Carbajal-Gomez, P J Obeso-Rodelo, J J Rangel-Magdaleno and J C Nez-Prez, Nonlinear Dynam. 82(4), 1879 (2015)MathSciNetCrossRefGoogle Scholar
  61. 61.
    J M Muoz-Pacheco, E Tlelo-Cuautle, E Flore-Tiro and R Trejo-Guerra, J. Appl. Res. Technol. 12(3), 459 (2014)CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Electrical and Electronics Engineering, Faculty of TechnologySakarya UniversitySerdivanTurkey

Personalised recommendations