, 90:63 | Cite as

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

  • Sen Zhang
  • Yicheng Zeng
  • Zhijun Li
  • Mengjiao Wang
  • Le Xiong


The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil’nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.


Grid multiwing attractor non-hyperbolic equilibrium point saddle-focus equilibrium point circuit implementation 


05.40.−a 05.40.Ac 05.45.Pq 05.45.Gg 



The work is supported by the National Natural Science Foundations of China under Grant No. 61471310, the Natural Science Foundations of Hunan Province, China under Grant No. 2015JJ2142, the Research Foundation of Education Bureau of Hunan Province, China under Grant No. 17C1530 and the Natural Science Foundation of Xiangtan University, China under Grant No. 15XZX33.


  1. 1.
    E N Lorenz, J. Atmos. Sci20, 130 (1963)ADSCrossRefGoogle Scholar
  2. 2.
    G R Chen and T Ueta, Int. J. Bifurc. Chaos 9, 1465 (1999)CrossRefGoogle Scholar
  3. 3.
    J H Lü and G R Chen, Int. J. Bifurc. Chaos 12, 659 (2002)CrossRefGoogle Scholar
  4. 4.
    C X Liu, T Liu, L Liu and K Liu, Chaos Solitons Fractals 22, 1031 (2004)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    W B Liu and G R Chen, Int. J. Bifurc. Chaos 13, 261 (2003)CrossRefGoogle Scholar
  6. 6.
    G Y Qi, G R Chen, S W Li and Y H Zhang, Int. J. Bifurc. Chaos 16, 859 (2006)CrossRefGoogle Scholar
  7. 7.
    S J Cang, G Y Qi and Z Q Chen, Nonlinear Dyn. 59, 515 (2010)CrossRefGoogle Scholar
  8. 8.
    S Dadras and H R Momeni, Phys. Lett. A 374, 1368 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    S M Yu, W K S Tang, J H Lü and G R Chen, Prceedings of the IEEE Int. Symp. Circuits Syst. (IEEE, 2008) pp. 768–771Google Scholar
  10. 10.
    G Grassi, F L Severance and D A Miller, Chaos Solitons Fractals 41, 284 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    B C Bao, X F Wang and J P Xu, Proceedings of the Int. Work. Chaos-Fractal Theor. Appl. (IEEE, 2010) pp. 211–215Google Scholar
  12. 12.
    S Dadras and H R Momeni, Chin. Phys. B 19, 60506 (2010)CrossRefGoogle Scholar
  13. 13.
    S Dadras, H R Momeni and G Y Qi, Nonlinear Dyn. 62, 391 (2010)CrossRefGoogle Scholar
  14. 14.
    Q Lai, Z H Guan, Y H Wu, F Liu and D X Zhang, Int. J. Bifurc. Chaos 23, 1350152 (2013)CrossRefGoogle Scholar
  15. 15.
    Y Huang, Acta Phys. Sinica 63, 080505 (2014)Google Scholar
  16. 16.
    S M Yu, W K S Tang, J H Lü and G R Chen, IEEE Trans. Circuits Syst. II Express Briefs 55, 1168 (2008)CrossRefGoogle Scholar
  17. 17.
    S M Yu, J H Lü, G R Chen and X H Yu, IEEE Trans. Circuits Syst. II Express Briefs 57, 803 (2010)CrossRefGoogle Scholar
  18. 18.
    X Zhou, C H Wang and X R Guo, Acta Phys. Sinica 61, 200506 (2012)Google Scholar
  19. 19.
    C X Zhang and S M Yu, Int. J. Circuit Theory Appl. 41, 221 (2013)CrossRefGoogle Scholar
  20. 20.
    Y Huang, P Zhang and W F Zhao, IEEE Trans. Circuits Syst. II: Express Briefs 62, 496 (2015)CrossRefGoogle Scholar
  21. 21.
    L P Chen, Y G He, X Lü and R C Wu, Pramana – J. Phys. 85, 91 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    Z J Li, M L Ma, M J Wang and Y C Zeng, AEU – Int. J. Electron. Commun. 71, 21 (2017)CrossRefGoogle Scholar
  23. 23.
    C H Wang, H Xia and L Zhou, Pramana – J. Phys. 88, 34 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    Z S Lin, S M Yu, J H Lü, S T Cai and G R Chen, IEEE Trans. Circuits Syst. Video Technol. 25, 1203 (2015)CrossRefGoogle Scholar
  25. 25.
    J H Lü and G R Chen, IEEE Trans. Automat. Contr. 50, 841 (2005)CrossRefGoogle Scholar
  26. 26.
    E Solak, R Rhouma and S Belghith, Opt. Commun. 283, 232 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    C P Silva, IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 40, 675 (1993)CrossRefGoogle Scholar
  28. 28.
    G L Li and X Y Chen, Commun. Nonlinear Sci. Numer. Simul. 14, 194 (2009)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    J C Sprott, Phys. Rev. E 50, R647 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    A Wolf, J B Swift, H L Swinney and J A Vastano, Physica D 16, 285 (1985)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    G A Gottwald and I Melbourne, Nonlinearity 22, 1367 (2009)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    S Dadras and H R Momeni, Phys. Lett. A 373, 3637 (2009)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    S Dadras, H R Momeni, G Y Qi and Z L Wang, Nonlinear Dyn. 67, 1161 (2012)CrossRefGoogle Scholar
  34. 34.
    Y Lin, C H Wang, H Z He and L L Zhou, Pramana – J. Phys. 86, 801 (2016)Google Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of Physics and Opotoelectric EngineeringXiangtan UniversityXiangtanChina
  2. 2.College of Information EngineeringXiangtan UniversityXiangtanChina

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