Skip to main content
SpringerLink
Log in

Detecting Critical Point of Fractional-Order Chemical System with Synchronization and Application to Image Enhancement Technique

  • Scientific Research Paper
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

In chemical reactions, not all the reactants interact immediately, and thus, there is a need to predict the critical point of a chemical reaction. In this paper, a new fractional-order Willamowski–R\(\ddot{o}\)ssler chemical system is studied to predict the critical point in the chemical reaction. Consequently, the existence of chaotic or non-equilibrium phenomenon in the proposed chemical system is confirmed. Also, the reaction ratio of the reactants in this chemical system is investigated. In addition, the necessary conditions are derived to synchronize two identical chemical systems by designing and applying sliding mode control. Further, we have shown that the proposed synchronization technique is faster than the existing synchronization technique by comparing sliding mode controller. In application point of view, the described fractional-order chemical system is applied for image enhancement technique. Finally, numerical simulations are provided to validate the effectiveness of the proposed theoretical approach.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Aghababa MP (2015) Design of hierarchical terminal sliding mode control scheme for fractional-order systems. Sci, Measure Technol, IET 9(1):122–133

    Article  Google Scholar 

  2. Balasubramaniam P, Muthukumar P, Ratnavelu K (2015) Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system. Nonlinear Dyn 80(1–2):249–267

    Article  MathSciNet  Google Scholar 

  3. Bodale I, Oancea VA (2015) Chaos control for willamowski-rössler model of chemical reactions. Chaos, Solit & Fractals 78:1–9

    Article  ADS  Google Scholar 

  4. Caputo M (1967) Linear models of dissipation whose q is almost frequency independent-ii. Geophys J Int 13(5):529–539

    Article  ADS  Google Scholar 

  5. Chen S and Zhao F (2016) The algorithm of fog-degraded traffic images enhancement based on fractional differential. 2016 IEEE Advanced Information Management, Communicates,Electronic and Automation Control Conference, pages 1949–1954

  6. Chen Y, Wei Y, Zhong H, Wang Y (2016) Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems. Nonlinear Dyn 50:1–11

    MathSciNet  MATH  Google Scholar 

  7. Delavari H, Lanusse P, Sabatier J (2013) Fractional order controller design for a flexible link manipulator robot. Asian J Control 15(3):783–795

    Article  MathSciNet  Google Scholar 

  8. Ding Y, Wang Z, Ye H (2012) Optimal control of a fractional-order hiv-immune system with memory. IEEE Trans Control Syst Technol 20(3):763–769

    Article  Google Scholar 

  9. El-Misiery A, Ahmed E (2006) On a fractional model for earthquakes. Appl Math Comput 178(2):207–211

    MathSciNet  MATH  Google Scholar 

  10. Epstein IR, Showalter K (1996) Nonlinear chemical dynamics: oscillations, patterns, and chaos. J Phys Chem 100(31):13132–13147

    Article  Google Scholar 

  11. Fatoorehchi H, Abolghasemi H, Zarghami R, Rach R (2015) Feedback control strategies for a cerium-catalyzed belousov-zhabotinsky chemical reaction system. Can J Chem Eng 92:1212–1221

    Article  Google Scholar 

  12. Garg V, Singh K (2012) An improved grunwald-letnikov fractional differential mask for image texture enhancement. Int J Adv Computer Sci Appl 3(3):130–135

    Google Scholar 

  13. Geysermans P, Nicolis G (1993) Thermodynamic fluctuations and chemical chaos in a well-stirred reactor: a master equation analysis. J Chem Phys 99(11):8964–8969

    Article  ADS  Google Scholar 

  14. Huang Y, Yang X-S (2005) Chaoticity of some chemical attractors: a computer assisted proof. J Math Chem 38(1):107–117

    Article  MathSciNet  Google Scholar 

  15. Izaguirre-Espinosa C, Muñoz-Vázquez AJ, Sánchez-Orta A, Parra-Vega V, Castillo P (2016) Attitude control of quadrotors based on fractional sliding modes: theory and experiments. IET Control Theory Appl 10(7):825–832

    Article  MathSciNet  Google Scholar 

  16. Lin T-C, Lee T-Y (2011) Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Trans Fuzzy Syst 19(4):623–635

    Article  Google Scholar 

  17. Matignon D (1996) Stability results for fractional differential equations with applications to control processing. Comput Eng Syst Appl 2:963–968

    Google Scholar 

  18. Muthukumar P, Balasubramaniam P, Ratnavelu K (2014) Synchronization and an application of a novel fractional order king cobra chaotic system. Chaos: Interdiscip J Nonlinear Sci 24(3):033105

    Article  MathSciNet  Google Scholar 

  19. Muthukumar P, Balasubramaniam P, Ratnavelu K (2015) Sliding mode control design for synchronization of fractional order chaotic systems and its application to a new cryptosystem. Int J Dyn Control 5:1–9

    MathSciNet  Google Scholar 

  20. Niu H, Zhang Q, Zhang Y (2002) The chaos synchronization of a singular chemical model and a williamowski-rossler model. Int J Inf Syst Sci 6(4):355–364

    Google Scholar 

  21. Poland D (1993) Cooperative catalysis and chemical chaos: a chemical model for the lorenz equations. Phys D: Nonlinear Phenom 65(1):86–99

    Article  ADS  Google Scholar 

  22. Rajagopal K, Karthikeyan A (2016) Chaos suppression of fractional order willamowski-rössler chemical system and its synchronization using sliding mode control. Nonlinear Eng 5(3):177–183

    Article  ADS  Google Scholar 

  23. Srivastava R, Srivastava P, Chattopadhyay J (2013) Chaos in a chemical system. Eur Phys J Special Top 222(3–4):777–783

    Article  ADS  Google Scholar 

  24. Tavazoei MS, Haeri M (2007) A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A 367(1):102–113

    Article  ADS  Google Scholar 

  25. Tékam GO, Kwuimy CK, Woafo P (2015) Analysis of tristable energy harvesting system having fractional order viscoelastic material. Chaos: Interdiscip J Nonlinear Sci 25(1):013112

    Article  MathSciNet  Google Scholar 

  26. Vadim IU (1977) Survey paper variable structure systems with sliding modes. IEEE Trans Autom Control 22(2):212–222

    Article  Google Scholar 

  27. Wang H, Li Q-S (2000) Microscopic dynamics of deterministic chemical chaos. J Phys Chem A 104(3):472–475

    Article  Google Scholar 

  28. Xu C, Wu Y (2015) Bifurcation and control of chaos in a chemical system. Appl Math Modell 39(8):2295–2310

    Article  MathSciNet  Google Scholar 

  29. Xu C-J, Wu Y-S (2014) Chaos control of a chemical chaotic system via time-delayed feedback control method. Int J Autom Comput 11(4):392–398

    Article  Google Scholar 

  30. Yawei L (2010) Remote sensing image enhancement based on fractional differential. 2012 Fourth International Conference on Computational and Information Sciences, pages 881–884

Download references

Acknowledgements

This work is supported by NFSC, UGC, New Delhi, File No. 82-1/2018 (SA-III), UGC-Ref. No.: 4071/ (CSIR-UGC NET JUNE 2018).

Author information

Authors and Affiliations

  1. Department of Mathematics, Gobi Arts and Science College (Bharathiar University), Gobichettipalayam, Erode, Tamil Nadu, 638 453, India

    P. Muthukumar

  2. Department of Mathematics, The Gandhigram Rural Institute - Deemed to be University, Gandhigram, Dindigul, Tamil Nadu, 624 302, India

    N. Ramesh Babu & P. Balasubramaniam

Authors
  1. P. Muthukumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Ramesh Babu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Balasubramaniam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Balasubramaniam.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Muthukumar, P., Babu, N.R. & Balasubramaniam, P. Detecting Critical Point of Fractional-Order Chemical System with Synchronization and Application to Image Enhancement Technique. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 91, 661–674 (2021). https://doi.org/10.1007/s40010-021-00763-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-021-00763-8

Keywords

Search

Navigation