Skip to main content
SpringerLink
Log in

An investigation on microscopic chaos controlling of identical chemical reactor system via adaptive controlled hybrid projective synchronization

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

Abstract

In this manuscript, a methodology is designed to investigate the microscopic chaos adaptive controlling in the dynamics of the chaotic chemical reactor system (CR-system) using hybrid projective synchronization (HPS) technique. Initially, an adaptive control design (ACD) has been presented and analyzed in a systematic manner for controlling the microscopic chaos phenomenon found in the CR-system which is essentially in accordance with Lyapunov stability analysis (LSA). The necessary asymptotic stability criterion for the state vectors of the discussed CR-system with uncertain parameters is determined by designing suitable control functions and simplified parameter updating law. Additionally, numerical simulation results using MATLAB software have been performed to illustrate the effective presentation of the proposed strategy. Simulation outcomes complement that the primary objective of controlling chaos in CR-system is attained both analytically and computationally. Furthermore, a comparative study with earlier published literature has been done.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. R.G. Harrison, D.J. Biswas, Nature 321, 394–401 (1986)

    Article  ADS  Google Scholar 

  2. J.P. Eckmann, S.O. Kamphurst, D. Ruelle, S. Ciliberto, Phys. Rev. A 34, 4971 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  3. L.F. Olsen, H. Degn, Quart. Rev. Biophys. 18, 165–225 (1985)

    Article  Google Scholar 

  4. L. Glass, M.C. Mackey, From clocks to chaos: the rhythms of life (Princeton University Press, Princeton, 1988), pp. 454–532

    Book  MATH  Google Scholar 

  5. J.C. Roux, R.H. Simoyi, H.L. Swinney, Phys. D 8, 257–266 (1983)

    Article  MathSciNet  Google Scholar 

  6. M.T.M. Koper, P. Gaspard, J.H. Sluters, J. Chem. Phys. 97, 8250–8260 (1992)

    Article  ADS  Google Scholar 

  7. S.K. Scott, Chemical chaos (Clarendon Press, Oxford, 1991)

    Google Scholar 

  8. E.N. Lorenz, J. Atmos. Sci. 20, 130–141 (1963)

    Article  ADS  Google Scholar 

  9. G. Huerta-Cuellar, E. Jiménez-López, E. Campos-Cantón, A.N. Pisarchik, Commun. Nonlinear Sci. Numer. Simulat. 19, 2740–2746 (2014)

    Article  ADS  Google Scholar 

  10. H.E. Gilardi-Velázquez, E. Campos-Cantón, Int. J. Mod. Phys. C 29, 1850020 (2018)

    Article  ADS  Google Scholar 

  11. P. Gaspard, Phys. A 263, 315–328 (1999)

    Article  Google Scholar 

  12. H. Wang, Q.S. Li, J. Phys. Chem. 104, 472–475 (2000)

    Article  Google Scholar 

  13. H. Wang, Q.S. Li, Sci. China Ser. B 43, 357–365 (2000)

    Article  Google Scholar 

  14. F. Sagues, I.R. Epstein, Dalton Trans. 7, 1201–1217 (2003)

    Article  Google Scholar 

  15. Y. huang, X.S. Yang, J.H. Sluters, J. Math. Chem. 38, 107–117 (2005)

    Article  MathSciNet  Google Scholar 

  16. L.G. Juan, G.M. Lampart, J. Math. Chem. 48, 66–71 (2010)

    Article  MathSciNet  Google Scholar 

  17. S. Marcantoni, S. Alipour, F. Benatti, R. Floreanini, A.T. Rezakhani, Sci. Rep. 7, 12447 (2017)

    Article  ADS  Google Scholar 

  18. S. Rasoulian, M. Shahrokhi, Iran. J. Chem. Eng. 29, 149–164 (2010)

    Google Scholar 

  19. N. Vasegh, F. Khellat, Int. J. Appl. Sci. Technol. 1, 233–243 (2011)

    Google Scholar 

  20. S. Kuntanapreeda, P.M. Marusak, Comput. Chem. Eng. 41, 10–23 (2012)

    Article  Google Scholar 

  21. R.R. Karri, V. Chimmiri, J.H. Sluters, Adv. Chem. Eng. Res. 2, 8250–8260 (2013)

    Google Scholar 

  22. M. Lawnik, M. Berezowski, Chem. Process Eng. 35, 387–396 (2014)

    Article  Google Scholar 

  23. D.T. Lynch, Chem. Eng. Sci. 48, 2103–2108 (1993)

    Article  Google Scholar 

  24. F. Manuel, P.-P. Lawnik, M. Perez-Molina, Chem. Eng. Sci. 74, 79–92 (2012)

    Article  Google Scholar 

  25. H. Mahara, T. Yamaguchi, P. Parmananda, Phys. Rev. E 89, 062913 (2014)

    Article  ADS  Google Scholar 

  26. K. Joshi, I. Tiwari, A. Nandi, P. Parmananda, Phys. Rev. E 98, 012218 (2018)

    Article  ADS  Google Scholar 

  27. L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  28. P.P. Singh, B.K. Roy, Ann. Rev. Control 45, 152–165 (2018)

    Article  Google Scholar 

  29. S. Banerjee, J. Kurths, Chaos and cryptography: a new dimension in secure communications, 2014

  30. S. Banerjee, L. Rondoni, M. Mitra, Applications of Chaos and nonlinear dynamics in science and engineering (Springer, Berlin) 3, 371–392 (2015)

  31. B.B. Sharma, A. Banshwar, M. Pathak, N.K. Sharma, A. Joshi, in Advances in Renewable Energy and Sustainable Environment (Springer), pp. 277–283

  32. S. Mukherjee, S.K. Palit, S. Banerjee, M.R.K. Ariffin, L. Rondoni, D.K. Bhattacharya, Phys. A 439, 93–102 (2015)

    Article  MathSciNet  Google Scholar 

  33. B.K. Patle, D.R.K. Parhi, A. Jagadeesh, S.K. Kashyap, Comput. Elect. Eng. 67, 708–728 (2018)

    Article  Google Scholar 

  34. X.J. Tong, M. Zhang, Z. Wang, Y. Liu, J. Ma, Optik 126, 2445–2452 (2015)

    Article  ADS  Google Scholar 

  35. K. Bouallegue, Neurocomputing 249, 28–47 (2017)

    Article  Google Scholar 

  36. D. Ghosh, A. Mukherjee, N.R. Das, B.N. Biswas, Optik 165, 275–287 (2018)

    Article  ADS  Google Scholar 

  37. B. Naderi, H. Kheiri, A. Heydari, Int. J. Nonli. Sci 27, 53–64 (2019)

    Google Scholar 

  38. B. Naderi, H. Kheiri, V. Vafaei, ISeCure 12, (2020)

  39. J.P. Singh, B.K. Roy, S. Jafari, Chaos Solit. Fract. 106, 243–257 (2018)

    Article  ADS  Google Scholar 

  40. S. Vaidyanathan, A. Sambas, S. Zhang, M.A. Mohamed, M. Mamat, Int. J. Eng. Technol. 7, 2430–2436 (2018)

    Article  Google Scholar 

  41. T. Khan, H. Chaudhary, Differ. Eqn. Dyn. Syst. 28, 515–526 (2020)

    Article  Google Scholar 

  42. A. Khan, H. Chaudhary, Arab. J. Math. 9, 597–611 (2020)

    Article  Google Scholar 

  43. A. Khan, H. Chaudhary, Emerging trends in information technology (Bloomsbury, New Delhi, 2019), pp. 174–184

    Google Scholar 

  44. S. Kumar, A.E. Matouk, H. Chaudhary, S. Kant, Int. J. Adapt. Control Signal Process. 35, 484–497 (2020)

    Article  Google Scholar 

  45. T. Khan, H. Chaudhary, Appln. Appl. Math. 15, 1135–1148 (2020)

    Google Scholar 

  46. T. Khan, H. Chaudhary, Poincare. J. Anal. Appl. 7, 211–225 (2020)

    MathSciNet  Google Scholar 

  47. A. Khan, H. Chaudhary, Appln. Appl. Math. 16, 117–138 (2021)

    Google Scholar 

  48. J.P. Singh, B.K. Roy, Optik 145, 209–217 (2017)

    Article  ADS  Google Scholar 

  49. J.P. Singh, B.K. Roy, Int. J. Dyn. Control 6, 529–538 (2018)

    Article  MathSciNet  Google Scholar 

  50. S. Jafari, V.T. Pham, T. Kapitaniak, Int. J. Bifur. Chaos 26, 1650031 (2016)

    Article  Google Scholar 

  51. S. Jafari, J.C. Sprott, F. Nazarimehr, Eur. Phys. J. Spec. Top. 224, 1469–1476 (2015)

    Article  Google Scholar 

  52. S. Vaidyanathan, Int. J. Chem. Tech. Res. 8, 740–749 (2015)

    Google Scholar 

  53. S. Vaidyanathan, Int. J. Chem. Tech. Res. 8, 759–768 (2015)

    Google Scholar 

  54. S. Vaidyanathan, Int. J. Pharm. Tech. Res. 8, 377–382 (2015)

    Google Scholar 

  55. H. Kheiri, B. Naderi, Dynamical behavior and synchronization of chaotic chemical reactors model (2014)

  56. M. Berezowski, Chem. Eng. Sci. 101, 451–453 (2013)

    Article  Google Scholar 

  57. M. Berezowski, D. Dubaj, Chaos Solit. Fract. 78, 22–25 (2015)

    Article  ADS  Google Scholar 

  58. Y. Dimotikalis, C. Skiadas, Chaos 2016 Book of Abstracts: Chaotic Modeling and Simulation International Conference (London, UK, 23–26 May 2016, ISAST, 2016)

  59. S. Vaidyanathan, C.H. Lien, Applications of Sliding Mode Control in Science and Engineering (Vol. 709, Springer, 2017)

  60. D. Mandragona, Hopf Bifurcation analysis of chaotic chemical reactor model, Honors in the major theses, 342, University of Central Florida, 2018. https://stars.library.ucf.edu/honorstheses/342

  61. J.F. Louvier-Hernandez, R. Rico-Martinez, P. Parmananda, Phys. Rev. E 65, 016203 (2001)

    Article  ADS  Google Scholar 

  62. E. Ramirez-Alvarez, R. Rico-Martinez, P. Parmananda, J. Phys. Chem. A 114, 12819–12824 (2010)

    Article  Google Scholar 

  63. J.E, Slotine, W. Li, Applied Nonlinear Control, (Prentice hall Englewood Cliffs NJ, 1991), Vol. 199

  64. A.W. Hubler, Helv. Phys. Acta. 62, 343–346 (1989)

    Google Scholar 

  65. R. Msinieri, J. Rehacek, Phys. Rev. Lett. 82, 3042 (1999)

    Article  ADS  Google Scholar 

  66. M. Hu, Z. Xu, R. Zhang, Commun. Nonli. Sci. Numer. Simul. 13, 456–464 (2008)

    Article  Google Scholar 

  67. B. Naderi, H. Kheiri, Optik 127, 2407–2412 (2016)

    Article  ADS  Google Scholar 

  68. G.C. Wu, D. Baleanu, Z.X. Lin, J. Vib. Control 22, 2092–2099 (2016)

    Article  MathSciNet  Google Scholar 

  69. D. Shevitz, B. Paden, IEEE Trans. Auto. Control 39, 1910–1914 (1994)

    Article  Google Scholar 

  70. L. Perko, Differ. Equ. Dyn. Syst., vol. 7 (Springer, Berlin, 2013)

    Google Scholar 

  71. N. Samardzija, L.D. Greller, E. Wasserman, J. Chem. Phys. 90, 2296–2304 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  72. P.P. Singh, B.K. Roy, Eur. Phys. J. Spec. Top. 228, 169–184 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Harindri Chaudhary & Ayub Khan

  2. Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah, Saudi Arabia

    Mohammad Sajid

Authors
  1. Harindri Chaudhary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ayub Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Sajid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Sajid.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chaudhary, H., Khan, A. & Sajid, M. An investigation on microscopic chaos controlling of identical chemical reactor system via adaptive controlled hybrid projective synchronization. Eur. Phys. J. Spec. Top. 231, 453–463 (2022). https://doi.org/10.1140/epjs/s11734-021-00404-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00404-6

Search

Navigation