IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v183y2024ics0960077924004235.html
   My bibliography  Save this article

Dynamic analysis and SDRE control applied in a mutating autocatalyst with chaotic behavior

Author

Listed:
  • Andrade, Dana I.
  • Specchia, Stefania
  • Fuziki, Maria E.K.
  • Oliveira, Jessica R.P.
  • Tusset, Angelo M.
  • Lenzi, Giane G.

Abstract

In this work, an autocatalytic chemical reactions model with mutation is investigated, and a nonlinear control is proposed to lead the system to a behavior that maintains the system with a desired behavior and with suppress the chaotic behavior. Numerical results considering a broad analysis of the system parameters confirmed the chaotic behavior using phase portraits, bifurcation diagrams and Lyapunov exponents. An analysis of the system behavior in fractional order considering the Atangana–Baleanu–Caputo operator was performed to include the memory effect in the system dynamics. The numerical results obtained demonstrated that the system is extremely sensitive to variations in the order of the derivative, taking the system from chaotic behavior to periodic behavior with small variations in the order of the derivative. The chaotic behavior of the system is proven in fractional order by the 0–1 test and a scale index based on the wavelets test. The proposed control demonstrated to be efficient in maintaining the main product (ethanol) output concentration at the desired level.

Suggested Citation

  • Andrade, Dana I. & Specchia, Stefania & Fuziki, Maria E.K. & Oliveira, Jessica R.P. & Tusset, Angelo M. & Lenzi, Giane G., 2024. "Dynamic analysis and SDRE control applied in a mutating autocatalyst with chaotic behavior," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004235
    DOI: 10.1016/j.chaos.2024.114871
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924004235
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114871?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nikolai A. Magnitskii, 2023. "Universal Bifurcation Chaos Theory and Its New Applications," Mathematics, MDPI, vol. 11(11), pages 1-20, May.
    2. Rastogi, Meenal & Shrivastava, Smriti, 2017. "Recent advances in second generation bioethanol production: An insight to pretreatment, saccharification and fermentation processes," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 330-340.
    3. Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
    4. Karagoz, Pınar & Bill, Roslyn M. & Ozkan, Melek, 2019. "Lignocellulosic ethanol production: Evaluation of new approaches, cell immobilization and reactor configurations," Renewable Energy, Elsevier, vol. 143(C), pages 741-752.
    5. Ali Allahem & Anitha Karthikeyan & Manisekaran Varadharajan & Karthikeyan Rajagopal, 2022. "Computational Model Of A Fractional-Order Chemical Reactor System And Its Control Using Adaptive Sliding Mode Control," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-11, December.
    6. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    7. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Melendez, Jesus R. & Mátyás, Bence & Hena, Sufia & Lowy, Daniel A. & El Salous, Ahmed, 2022. "Perspectives in the production of bioethanol: A review of sustainable methods, technologies, and bioprocesses," Renewable and Sustainable Energy Reviews, Elsevier, vol. 160(C).
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. Rongwei Guo & Yaru Zhang & Cuimei Jiang, 2021. "Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance," Mathematics, MDPI, vol. 9(8), pages 1-12, April.
    4. Hanshuo Qiu & Xiangzi Zhang & Huaixiao Yue & Jizhao Liu, 2023. "A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption," Mathematics, MDPI, vol. 11(19), pages 1-29, September.
    5. Yang, Guang & Wang, Jianlong, 2018. "Various additives for improving dark fermentative hydrogen production: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 95(C), pages 130-146.
    6. Hasib Khan & Jehad Alzabut & Haseena Gulzar & Osman Tunç & Sandra Pinelas, 2023. "On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    7. Cheng, F. & Brewer, C.E., 2021. "Conversion of protein-rich lignocellulosic wastes to bio-energy: Review and recommendations for hydrolysis + fermentation and anaerobic digestion," Renewable and Sustainable Energy Reviews, Elsevier, vol. 146(C).
    8. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Shoaib, Muhammad & Kiani, Adiqa Kausar, 2022. "Fractional order Lorenz based physics informed SARFIMA-NARX model to monitor and mitigate megacities air pollution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    9. Dhiman, Saurabh Sudha & David, Aditi & Braband, Vanessa W. & Hussein, Abdulmenan & Salem, David R. & Sani, Rajesh K., 2017. "Improved bioethanol production from corn stover: Role of enzymes, inducers and simultaneous product recovery," Applied Energy, Elsevier, vol. 208(C), pages 1420-1429.
    10. Urszula Dziekońska-Kubczak & Joanna Berłowska & Piotr Dziugan & Piotr Patelski & Katarzyna Pielech-Przybylska & Maria Balcerek, 2018. "Nitric Acid Pretreatment of Jerusalem Artichoke Stalks for Enzymatic Saccharification and Bioethanol Production," Energies, MDPI, vol. 11(8), pages 1-17, August.
    11. Machado, R.L. & Abreu, M.R., 2024. "Multi-objective optimization of the first and second-generation ethanol supply chain in Brazil using the water-energy-food-land nexus approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 193(C).
    12. Jin, Xianchun & Ma, Jiangshan & Song, Jianing & Liu, Gao-Qiang, 2020. "Saccharification and detoxification of Na2CO3 pretreated rice straw with on-site manufactured enzymes secreted by Aspergillus fumigatus to enhance bioethanol yield," Renewable Energy, Elsevier, vol. 166(C), pages 117-124.
    13. Huzir, Nurhamieza Md & Aziz, Md Maniruzzaman A. & Ismail, S.B. & Abdullah, Bawadi & Mahmood, Nik Azmi Nik & Umor, N.A. & Syed Muhammad, Syed Anuar Faua’ad, 2018. "Agro-industrial waste to biobutanol production: Eco-friendly biofuels for next generation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 94(C), pages 476-485.
    14. Nikolay M. Evstigneev & Nikolai A. Magnitskii, 2023. "Bifurcation Analysis Software and Chaotic Dynamics for Some Problems in Fluid Dynamics Laminar–Turbulent Transition," Mathematics, MDPI, vol. 11(18), pages 1-25, September.
    15. Tinôco, Daniel & Genier, Hugo Leonardo André & da Silveira, Wendel Batista, 2021. "Technology valuation of cellulosic ethanol production by Kluyveromyces marxianus CCT 7735 from sweet sorghum bagasse at elevated temperatures," Renewable Energy, Elsevier, vol. 173(C), pages 188-196.
    16. Guo, Tianyu & Yu, Yan & Wan, Zhangmin & Zargar, Shiva & Wu, Jie & Bi, Ran & Sokhansanj, Shahabaddine & Tu, Qingshi & Rojas, Orlando J., 2022. "Energy pellets from whole-wheat straw processed with a deep eutectic solvent: A comprehensive thermal, molecular and environmental evaluation," Renewable Energy, Elsevier, vol. 194(C), pages 902-911.
    17. Annamalai Meenakshi & Elango Renuga & Robert Čep & Krishnasamy Karthik, 2024. "Analysis of Caputo Fractional-Order Co-Infection COVID-19 and Influenza SEIR Epidemiology by Laplace Adomian Decomposition Method," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    18. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    19. Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    20. Pho, Kim-Hung & Heydari, M.H. & Tuan, Bui Anh & Mahmoudi, Mohammad Reza, 2020. "Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004235. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.