IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v169y2023ics0960077923001996.html
   My bibliography  Save this article

Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator

Author

Listed:
  • Deepika, S.
  • Veeresha, P.

Abstract

The chaotic waterwheel model is a mechanical model that exhibits chaos and is also a practical system that justifies the Lorenz system. The chaotic waterwheel model (or Malkus waterwheel model) is modified with the addition of asymmetric water inflow to the system. The hereditary property of the modified chaotic waterwheel model is analyzed to determine the system’s stability and identify the parameter that contributes to the stability We also examine the factor that leads to the bifurcation. We determine the well-posed nature of the modified system. The modified chaotic waterwheel model is defined with the Caputo fractional operator. The existence and uniqueness, boundedness, stability, Lyapunov stability, and numerical simulation are studied for the modified fractional waterwheel model. The bifurcation parameter and Lyapunov exponent are examined to study the chaotic nature of the system with respect to the fractional order. The nature of the system is captured with the help of the efficient numerical approach Adams–Bashforth–Moulton Method. The numerical approach demonstrates that the chaotic nature of the modified chaotic waterwheel is changed into unstable nature, which could further reduce to the stable case with suitable values of the parameter. This analysis is justified with the help of Lyapunov exponent. We consider irrational order (π,e) in the present work to illustrate the reliability of fractional order.

Suggested Citation

  • Deepika, S. & Veeresha, P., 2023. "Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001996
    DOI: 10.1016/j.chaos.2023.113298
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923001996
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113298?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. David Levy, 1994. "Chaos theory and strategy: Theory, application, and managerial implications," Strategic Management Journal, Wiley Blackwell, vol. 15(S2), pages 167-178, June.
    2. J. A. Tenreiro Machado & Manuel F. Silva & Ramiro S. Barbosa & Isabel S. Jesus & Cecília M. Reis & Maria G. Marcos & Alexandra F. Galhano, 2010. "Some Applications of Fractional Calculus in Engineering," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-34, November.
    3. Gao, Wei & Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D. G. & Kumar, Pushpendra, 2020. "A new study of unreported cases of 2019-nCOV epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Xuan Liu & Mati Ur Rahman & Muhammad Arfan & Fairouz Tchier & Shabir Ahmad & Mustafa Inc & Lanre Akinyemi, 2022. "Fractional Mathematical Modeling To The Spread Of Polio With The Role Of Vaccination Under Non-Singular Kernel," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-17, August.
    5. Iyiola, Olaniyi & Oduro, Bismark & Akinyemi, Lanre, 2021. "Analysis and solutions of generalized Chagas vectors re-infestation model of fractional order type," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Akinlar, Mehmet Ali & Tchier, Fairouz & Inc, Mustafa, 2020. "Chaos control and solutions of fractional-order Malkus waterwheel model," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Skwara, Urszula & Mozyrska, Dorota & Aguiar, Maira & Stollenwerk, Nico, 2024. "Dynamics of vector-borne diseases through the lens of systems incorporating fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Chakraborty, Arkaprovo & Veeresha, P., 2024. "Investigating the dynamics, synchronization and control of chaos within a transformed fractional Samardzija–Greller framework," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Ali, Khalid K. & Wazwaz, Abdul-Majid & Maneea, M., 2024. "Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

    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. Tammy E. Beck & Donde Ashmos Plowman, 2009. "Experiencing Rare and Unusual Events Richly: The Role of Middle Managers in Animating and Guiding Organizational Interpretation," Organization Science, INFORMS, vol. 20(5), pages 909-924, October.
    2. Arianna Dal Forno & Ugo Merlone, 2021. "Envy effects on conflict dynamics in supervised work groups," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 755-779, December.
    3. Zhao, LiuWei & Chang, Jianwei & DU, Jianguo, 2019. "Dynamics analysis on competition between manufacturing and remanufacturing in context of government subsidies," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 119-128.
    4. Henkel, Joachim & Rønde, Thomas & Wagner, Marcus, 2015. "And the winner is—Acquired. Entrepreneurship as a contest yielding radical innovations," Research Policy, Elsevier, vol. 44(2), pages 295-310.
    5. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    6. Franklin M. Lartey, 2020. "Chaos, Complexity, and Contingency Theories: A Comparative Analysis and Application to the 21st Century Organization," Journal of Business Administration Research, Journal of Business Administration Research, Sciedu Press, vol. 9(1), pages 44-51, April.
    7. Wagner, Marcus, 2008. "Technology sourcing by large incumbents through acquisition of small firms," SFB 649 Discussion Papers 2008-055, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    9. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    11. Mingers, John & White, Leroy, 2010. "A review of the recent contribution of systems thinking to operational research and management science," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1147-1161, December.
    12. Moncaleano, Carlos Javier Martínez, 2018. "Teoría del Caos y Estrategia Empresarial," Revista Tendencias, Universidad de Narino, vol. 19(1), pages 204-214, January.
    13. Izadbakhsh, Alireza & Nikdel, Nazila, 2021. "Chaos synchronization using differential equations as extended state observer," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    14. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    15. Whitby, Simon & Parker, David & Tobias, Andrew, 2001. "Non-linear dynamics and duopolistic competition: a R&D model and simulation," Journal of Business Research, Elsevier, vol. 51(3), pages 179-191, March.
    16. Godfrey Cadogan, 2014. "Chaos in a Large System of Decision‐Makers with Heterogeneous Beliefs with Application to Index Option Prices," Systems Research and Behavioral Science, Wiley Blackwell, vol. 31(4), pages 487-501, July.
    17. repec:hum:wpaper:sfb649dp2007-063 is not listed on IDEAS
    18. Rønde, Thomas & Henkel, Joachim & Wagner, Marcus, 2010. "And the Winner Is--Acquired: Entrepreneurship as a Contest with Acquisition as the Prize," CEPR Discussion Papers 8147, C.E.P.R. Discussion Papers.
    19. Deng, Guoting & Yang, Yin & Tohidi, Emran, 2021. "High accurate pseudo-spectral Galerkin scheme for pantograph type Volterra integro-differential equations with singular kernels," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    20. Mary Han & Bill McKelvey, 2016. "How to Grow Successful Social Entrepreneurship Firms? Key Ideas from Complexity Theory," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 243-280, September.
    21. Marcello Tonelli & Nicolò Cristoni, 2015. "Can GRI Light Up the Future of Mankind?," Proceedings of International Academic Conferences 2503903, International Institute of Social and Economic Sciences.

    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:169:y:2023:i:c:s0960077923001996. 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.