Skip to main content
SpringerLink
Log in

A novel class of chaotic systems with different shapes of equilibrium and microcontroller-based cost-effective design for digital applications

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

Constructing chaotic systems with infinite equilibrium points has been of interest in recent years. Many chaotic systems with equilibrium points located on open and closed curve have been published in the literature. A few of these systems show artistic equilibrium shapes. In this paper we propose the generalized model of a third-order chaotic system. It shows different shapes of equilibria by a suitable selection of nonlinear function, while the other nonlinearities of the system are not changed. One of the proposed chaotic models, which is taken as an example, shows multistability with co-existing attractors. The electronic circuit implementation of the proposed system is also presented. Additionally, for digital engineering applications, the microcontroller-based design of the system is conducted as well. The numerical results, circuit implementation outputs and the results of the microcontroller-based design match with each other.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Jafari, J.C. Sprott, Chaos, Solitons Fractals 57, 79 (2013) 77

    Article  ADS  MathSciNet  Google Scholar 

  2. K. Rajagopal, S. Jafari, A. Karthikeyan, A. Srinivasan, B. Ayele, Circ. Syst. Signal Proces. (2018) https://doi.org/10.1007/s00034-018-0750-7

  3. C. Li, J. Sprott, Phys. Lett. A 378, 178 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  4. K. Barati, S. Jafari, J.C. Sprott, V.-T. Pham, Int. J. Bifurc. Chaos 26, 1630034 (2016)

    Article  Google Scholar 

  5. C. Li, J.C. Sprott, Z. Yuan, H. Li, Int. J. Bifurc. Chaos 25, 1530025 (2015)

    Article  Google Scholar 

  6. Y. Chen, Q. Yang, Math. Comput. Simul. 112, 40 (2015)

    Article  Google Scholar 

  7. V.-T. Pham, S. Jafari, C. Volos, S. Vaidyanathan, T. Kapitaniak, Optik 127, 9111 (2016)

    Article  ADS  Google Scholar 

  8. T. Gotthans, J. Petržela, Nonlinear Dyn 81, 1143 (2015)

    Article  Google Scholar 

  9. T. Gotthans, J.C. Sprott, J. Petrzela, Int. J. Bifurc. Chaos 26, 1650137 (2016)

    Article  Google Scholar 

  10. S.T. Kingni, V.-T. Pham, S. Jafari, P. Woafo, Chaos, Solitons Fractals 99, 209 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  11. V.-T. Pham, S. Jafari, X. Wang, J. Ma, Int. J. Bifurc. Chaos 26, 1650069 (2016)

    Article  Google Scholar 

  12. V.-T. Pham, S. Jafari, C. Volos, Optik 131, 343 (2017)

    Article  ADS  Google Scholar 

  13. J. Liu, W. Zhang, Optik 124, 5528 (2013)

    Article  ADS  Google Scholar 

  14. M.S. Azzaz, C. Tanougast, S. Sadoudi, R. Fellah, A. Dandache, Commun. Nonlinear Sci. Numer. Simul. 18, 1792 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  15. W. Yu, Commun. Nonlinear Sci. Numer. Simul. 16, 2880 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  16. M. Alçin, I. Pehlivan, I. Koyuncu, Optik 127, 5500 (2016)

    Article  ADS  Google Scholar 

  17. E. Tlelo-Cuautle, J. Rangel-Magdaleno, A. Pano-Azucena, P. Obeso-Rodelo, J.C. Nuñez-Perez, Commun. Nonlinear Sci. Numer. Simul. 27, 66 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  18. D.K. Shah, R.B. Chaurasiya, V.A. Vyawahare, K. Pichhode, M.D. Patil, Int. J. Electron. Commun. 78, 245 (2017)

    Article  Google Scholar 

  19. R. Caponetto, A. Di Mauro, L. Fortuna, M. Frasca, Int. J. Bifurc. Chaos 15, 1829 (2005)

    Article  Google Scholar 

  20. R. Kilic, F.Y. Dalkiran, Int. J. Bifurc. Chaos 19, 1339 (2009)

    Article  Google Scholar 

  21. F.Y. Dalkiran, J.C. Sprott, Int. J. Bifurc. Chaos 26, 1650189 (2016)

    Article  Google Scholar 

  22. V. Guglielmi, P. Pinel, D. Fournier-Prunaret, A.-K. Taha, Chaos, Solitons Fractals 42, 2135 (2009)

    Article  ADS  Google Scholar 

  23. C.K. Volos, J. Comput. Model. 3, 115 (2013)

    Google Scholar 

  24. R. Chiu, M. Mora-Gonzalez, D. Lopez-Mancilla, IERI Proc. 4, 247 (2013)

    Article  Google Scholar 

  25. L. Acho, J. Franklin Inst. 352, 3113 (2015)

    Article  MathSciNet  Google Scholar 

  26. S. Kaçar, Optik 127, 9551 (2016)

    Article  ADS  Google Scholar 

  27. E. Zambrano-Serrano, J. Muñoz-Pacheco, E. Campos-Cantón, Int. J. Electron. Commun. 79, 43 (2017)

    Article  Google Scholar 

  28. V.T. Pham, S. Jafari, C. Volos, T. Kapitaniak, Chaos, Solitons Fractals 93, 58 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  29. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  30. T. Kapitaniak, J. Sound Vib. 102, 440 (1985)

    Article  ADS  Google Scholar 

  31. B. Blazejczyk-Okolewska, T. Kapitaniak, Chaos, Solitons Fractals 7, 1455 (1996)

    Article  ADS  Google Scholar 

  32. Y. Maistrenko, T. Kapitaniak, P. Szuminski, Phys. Rev. E 56, 6393 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  33. B. Blazejczyk-Okolewska, T. Kapitaniak, Chaos, Solitons Fractals 9, 1439 (1998)

    Article  ADS  Google Scholar 

  34. A. Silchenko, T. Kapitaniak, V. Anishchenko, Phys. Rev. E 59, 1593 (1999)

    Article  ADS  Google Scholar 

  35. A. Chudzik, P. Perlikowski, A. Stefanski, T. Kapitaniak, Int. J. Bifurc. Chaos 21, 1907 (2011)

    Article  Google Scholar 

  36. C. Li, J. Sprott, Int. J. Bifurc. Chaos 24, 1450034 (2014)

    Article  Google Scholar 

  37. V.-T. Pham, C. Volos, S. Jafari, T. Kapitaniak, J. Circ. Syst. Comput. 27, 1850066 (2017)

    Article  Google Scholar 

  38. V.-T. Pham, C. Volos, S. Jafari, T. Kapitaniak, Nonlinear Dyn. 87, 2001 (2017)

    Article  Google Scholar 

  39. Q. Lai, S. Chen, Int. J. Control, Autom. Syst. 14, 1124 (2016)

    Article  Google Scholar 

  40. Q. Lai, L. Wang, Optik 127, 5400 (2016)

    Article  ADS  Google Scholar 

  41. Q. Lai, A. Akgul, X.-W. Zhao, H. Pei, Int. J. Bifurc. Chaos 27, 1750142 (2017)

    Article  Google Scholar 

  42. J.C. Sprott, S. Jafari, A.J.M. Khalaf, T. Kapitaniak, Eur. Phys. J. ST 226, 1979 (2017)

    Article  Google Scholar 

  43. B. Bao, T. Jiang, Q. Xu, M. Chen, H. Wu, Y. Hu, Nonlinear Dyn. 86, 1711 (2016)

    Article  Google Scholar 

  44. B.-C. Bao, Q. Xu, H. Bao, M. Chen, Electron. Lett. 52, 1008 (2016)

    Article  Google Scholar 

  45. B. Bao, H. Bao, N. Wang, M. Chen, Q. Xu, Chaos, Solitons Fractals 94, 102 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  46. B. Bao, T. Jiang, G. Wang, P. Jin, H. Bao, M. Chen, Nonlinear Dyn. 89, 1157 (2017)

    Article  Google Scholar 

  47. J. Ma, X. Wu, R. Chu, L. Zhang, Nonlinear Dyn. 76, 1951 (2014)

    Article  Google Scholar 

  48. C. Li, I. Pehlivan, J.C. Sprott, A. Akgul, IEICE Electron. Express 12, 20141116 (2015)

    Article  Google Scholar 

  49. Q. Li, H. Zeng, J. Li, Nonlinear Dyn. 79, 2295 (2015)

    Article  Google Scholar 

  50. A. Akgul, I. Moroz, I. Pehlivan, S. Vaidyanathan, Optik 127, 5491 (2016)

    Article  ADS  Google Scholar 

  51. A. Akgul, H. Calgan, I. Koyuncu, I. Pehlivan, A. Istanbullu, Nonlinear Dyn. 84, 481 (2016)

    Article  Google Scholar 

  52. Z. Wei, I. Moroz, J. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101 (2017)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Nonlinear Dynamics, Defence University, Bishoftu, Ethiopia

    Karthikeyan Rajagopal & Anitha Karthikeyan

  2. Department of Electronic & Automation, Vocational School of Hacıbektaş, Nevşehir Hacı Bektaş Veli University, 50800 Hacıbektaş, Nevşehir, Turkey

    Serdar Çiçek

  3. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    Viet-Thanh Pham

  4. Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran

    Sajad Jafari

Authors
  1. Karthikeyan Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Serdar Çiçek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Viet-Thanh Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sajad Jafari
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anitha Karthikeyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karthikeyan Rajagopal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rajagopal, K., Çiçek, S., Pham, VT. et al. A novel class of chaotic systems with different shapes of equilibrium and microcontroller-based cost-effective design for digital applications. Eur. Phys. J. Plus 133, 231 (2018). https://doi.org/10.1140/epjp/i2018-12053-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2018-12053-7

Search

Navigation