Skip to main content
SpringerLink
Log in

Network dynamics of a periodically forced chemical system and its application for tuning PID controller with time-delay systems

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, network dynamics are investigated in a periodically forced chemical system. At the same time, the ring network and ring-star network based on the periodically forced chemical system are designed. The chaotic dynamics of the ring network and ring-star network are analyzed by using the Lyapunov exponent spectrum, bifurcation diagram and correlation function. We show that the coupling strength of ring network has an important influence on chaotic dynamics and synchronization. By comparing ten, eleven and 100 nodes, we find that the bifurcation path of the ring-star network is robust to the number of nodes, which is different from the ring network. In addition, the ring-star network in comparison with the ring network achieved chaotic complete synchronization among all nodes. Finally, we proposed a new chaotic whale optimization (CWO) algorithm using the randomness of the ring-star network. It is used to tune the parameters of the PID controller with large time-delay systems. The simulation results show that the proposed CWO algorithm presents better performance than other available algorithms in the literature.

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
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

Data will be made available on reasonable request.

References

  1. Mahdieh, A.R., Mahdi, Y.: Optimum design of fractional order PID controller using chaotic firefly algorithms for a control CSTR system. Asian J. Control 21, 2245–2255 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ravichandran, D., Praveenkumar, P., Rayappan, J.B.B., Amirtharajan, R.: DNA chaos blend to secure medical privacy. IEEE Trans. Nanobiosci. 16, 850–858 (2017)

    Article  Google Scholar 

  3. Flores-Vergara, A., García-Guerrero, E.E., Inzunza-González, E., et al.: Implementing a chaotic cryptosystem in a 64-bit embedded system by using multiple-precision arithmetic. Nonlinear Dyn. 96, 497–516 (2019)

    Article  MATH  Google Scholar 

  4. Zheng, J., Hu, H., Xiang, X.: Applications of symbolic dynamics in counteracting the dynamical degradation of digital chaos. Nonlinear Dyn. 94, 1535–1546 (2018)

    Article  Google Scholar 

  5. Bao, H., Hu, A., Liu, W., Bao, B.: Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Trans. Neural Netw. Learn. Syst. 31, 502–511 (2020)

    Article  Google Scholar 

  6. Khokhar, B., Dahiya, S., Parmar, K.P.S.: Load frequency control of a microgrid employing a 2D sine logistic map based chaotic sine cosine algorithm. Appl. Soft Comput. 109, 107564 (2021)

    Article  Google Scholar 

  7. Asgharnia, A., Shahnazi, R., Jamali, A.: Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms. ISA Trans. 79, 27–44 (2018)

    Article  Google Scholar 

  8. Pham, Q.V., Mirjalili, S., Kumar, N., Alazab, M., Hwang, W.J.: Whale optimization algorithm with applications to resource allocation in wireless networks. IEEE Trans. Veh. Technol. 69, 4285–4297 (2020)

    Article  Google Scholar 

  9. Guha, D., Roy, P.K., Banerjee, S.: Performance evolution of different controllers for frequency regulation of a hybrid energy power system employing chaotic crow search algorithm. ISA Trans. 120, 128–146 (2022)

    Article  Google Scholar 

  10. Misaghi, M., Yaghoobi, M.: Improved invasive weed optimization algorithm (IWO) based on chaos theory for optimal design of PID controller. J. Comput. Des. Eng. 6, 284–295 (2019)

    Google Scholar 

  11. Micev, M., Ćalasan, M., Oliva, D.: Fractional order PID controller design for an AVR system using chaotic yellow saddle goatfish algorithm. Mathematics 8, 1182 (2020)

    Article  Google Scholar 

  12. Çelik, E.: Incorporation of stochastic fractal search algorithm into efficient design of PID controller for an automatic voltage regulator system. Neural Comput. Appl. 30, 1991–2002 (2018)

    Article  Google Scholar 

  13. Li, C., Feng, B., Li, S., Kurths, J., Chen, G.: Dynamic analysis of digital chaotic maps via state-mapping networks. IEEE Trans. Circuits Syst. I Regul. Pap. 66, 2322–2335 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, X., Liu, P.: A new full chaos coupled mapping lattice and its application in privacy image encryption. IEEE Trans. Circuits Syst. I Regul. Pap. 69, 1291–1301 (2021)

    Article  Google Scholar 

  15. Ming, H., Hu, H., Zheng, J.: Analysis of a new coupled hyperchaotic model and its topological types. Nonlinear Dyn. 105, 1937–1952 (2021)

    Article  Google Scholar 

  16. Bao, B., Rong, K., Li, H., Li, K., Zhang, X.: Memristor-coupled logistic hyperchaotic map. IEEE Trans. Circuits Syst. II Express Briefs 68, 2992–2996 (2021)

    Google Scholar 

  17. Stankevich, N.V., Dvorak, A., Astakhov, V., Jaros, P., Kapitaniak, M., Perlikowski, P., Kapitaniak, T.: Chaos and hyperchaos in coupled antiphase driven Toda oscillators. Regul. Chaotic Dyn. 23, 120–126 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zou, C., Zhang, Q., Wei, X.: Compilation of a coupled hyper-chaotic Lorenz system based on DNA strand displacement reaction network. IEEE Trans. Nanobiosci. 20, 92–104 (2020)

    Article  Google Scholar 

  19. Kadir, A., Aili, M., Sattar, M.: Color image encryption scheme using coupled hyper chaotic system with multiple impulse injections. Optik 129, 231–238 (2017)

    Article  Google Scholar 

  20. Fouda, E., Sabat, S.L.: A multiplierless hyperchaotic system using coupled Duffing oscillators. Commun. Nonlinear Sci. Numer. Simul. 20, 24–31 (2015)

    Article  Google Scholar 

  21. Wang, S., Hu, G., Zhou, H.: A one-way coupled chaotic map lattice based self-synchronizing stream cipher. Commun. Nonlinear Sci. Numer. Simul. 19, 905–913 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Qu, S., Zhang, Q., Zhang, J., Sun, J., Wang, X.: Performance analysis on distributed storage systems in ring networks. IEEE Trans. Veh. Technol. 69, 7762–7777 (2020)

    Google Scholar 

  23. Zhao, X., Liu, J., Chen, G., Chai, L., Wang, D.: Dynamics and synchronization of complex-valued ring networks. Int. J. Bifurc. Chaos 32, 2230011 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  24. Chai, L., Liu, J., Chen, G., Zhao, X.: Dynamics and synchronization of a complex-valued star network. Sci. China Technol. Sci. 64, 2729–2743 (2021)

    Article  Google Scholar 

  25. Sabarathinam, S., Prasad, A.: Generalized synchronization in a conservative and nearly conservative systems of star network. Chaos 28, 113107 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  26. Muni, S.S., Provata, A.: Chimera states in ring-star network of Chua circuits. Nonlinear Dyn. 101, 2509–2521 (2020)

    Article  Google Scholar 

  27. Muni, S.S., Fatoyinbo, H.O., Ghosh, I.: Dynamical effects of electromagnetic flux on chialvo neuron map: nodal and network behaviors. Int. J. Bifurc. Chaos 32, 2230020 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wang, M., Hou, Z., Xin, H.: Internal noise-enhanced phase synchronization of coupled chemical chaotic oscillators. J. Phys. A 38, 145 (2004)

    Article  MATH  Google Scholar 

  29. Epstein, I.R.: Experimental and theoretical studies of coupled chemical oscillators. React. Kinet. Catal. Lett. 42, 241–252 (1990)

    Article  Google Scholar 

  30. Tinsley, M.R., Nkomo, S., Showalter, K.: Chimera and phase-cluster states in populations of coupled chemical oscillators. Nat. Phys. 8, 662–665 (2012)

    Article  Google Scholar 

  31. Yoshimoto, M., Yoshikawa, K., Mori, Y.: Coupling among three chemical oscillators: synchronization, phase death, and frustration. Phys. Rev. E 47, 864 (1993)

    Article  Google Scholar 

  32. Holló, G., Lagzi, I.: Autonomous chemical modulation and unidirectional coupling in two oscillatory chemical systems. J. Phys. Chem. A 123, 1498–1504 (2019)

    Article  Google Scholar 

  33. Geysermans, P., Baras, F.: Particle simulation of chemical chaos. J. Chem. Phys. 105, 1402–1408 (1996)

    Article  Google Scholar 

  34. Sriram, K.: Effects of positive electrical feedback in the oscillating belousov-zhabotinsky reaction: experiments and simulations. Chaos Solitons Fractals 28, 1055–1066 (2006)

    Article  MATH  Google Scholar 

  35. Edwards, M.A., Williams, C.G., Whitworth, A.L., Unwin, P.R.: Scanning ion conductance microscopy: a model for experimentally realistic conditions and image interpretation. Anal. Chem. 81, 4482–4492 (2009)

    Article  Google Scholar 

  36. Kurin-Csorgei, K., Epstein, I.R., Orban, M.: Systematic design of chemical oscillators using complexation and precipitation equilibria. Nature 433, 139–142 (2005)

    Article  Google Scholar 

  37. Wong, A.S., Postma, S.G., Vialshin, I.N., Semenov, S.N., Huck, W.T.: Influence of molecular structure on the properties of out-of-equilibrium oscillating enzymatic reaction networks. J. Am. Chem. Soc. 137, 12415–12420 (2015)

    Article  Google Scholar 

  38. Bashkirtseva, I.A., Ryashko, L.B., Pisarchik, A.N.: Ring of map-based neural oscillators: from order to chaos and back. Chaos Solitons Fractals 136, 109830 (2020)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No: 61672124), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund (No: MMJJ20170203), Liaoning Province Science and Technology Innovation Leading Talents Program Project (No: XLYC1802013), Key R&D Projects of Liaoning Province (No: 2019020105-JH2/103), Jinan City 20 universities Funding Projects Introducing Innovation Team Program (No: 2019GXRC031), Research Fund of Guangxi Key Lab of Multi-source Information Mining & Security (No: MIMS20-M-02).

Funding

The funding was provided by the National Natural Science Foundation of China, 61672124, Xingyuan Wang, Jilin Scientific and Technological Development Program, MMJJ20170203, Xingyuan Wang, Liaoning Province Science and Technology Innovation Leading Talents Program Project, XLYC1802013, Xingyuan Wang, Jinan City 20 universities’ Funding Projects Introducing Innovation Team Program, 2019GXRC031, Xingyuan Wang, Guangxi Key Laboratory of Multi-Source Information Mining and Security, MIMS20-M-02, Xingyuan Wang.

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, Liaoning, China

    Xiu Zhao, Xingyuan Wang, Yining Su & Salahuddin Unar

Authors
  1. Xiu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingyuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yining Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Salahuddin Unar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiu Zhao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, X., Wang, X., Su, Y. et al. Network dynamics of a periodically forced chemical system and its application for tuning PID controller with time-delay systems. Nonlinear Dyn 111, 13601–13617 (2023). https://doi.org/10.1007/s11071-023-08534-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08534-3

Keywords

Search

Navigation