IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p912-d1064730.html
   My bibliography  Save this article

Multidigraph Autocatalytic Set for Modelling Complex Systems

Author

Listed:
  • Nor Kamariah Kasmin

    (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia)

  • Tahir Ahmad

    (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia)

  • Amidora Idris

    (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia)

  • Siti Rahmah Awang

    (Faculty of Management, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia)

  • Mujahid Abdullahi

    (Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia
    Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University, 048 SLU Kafin Hausa, Kano 700271, Nigeria)

Abstract

The motion of solid objects or even fluids can be described using mathematics. Wind movements, turbulence in the oceans, migration of birds, pandemic of diseases and all other phenomena or systems can be understood using mathematics, i.e., mathematical modelling. Some of the most common techniques used for mathematical modelling are Ordinary Differential Equation (ODE), Partial Differential Equation (PDE), Statistical Methods and Neural Network (NN). However, most of them require substantial amounts of data or an initial governing equation. Furthermore, if a system increases its complexity, namely, if the number and relation between its components increase, then the amount of data required and governing equations increase too. A graph is another well-established concept that is widely used in numerous applications in modelling some phenomena. It seldom requires data and closed form of relations. The advancement in the theory has led to the development of a new concept called autocatalytic set (ACS). In this paper, a new form of ACS, namely, multidigraph autocatalytic set (MACS) is introduced. It offers the freedom to model multi relations between components of a system once needed. The concept has produced some results in the form of theorems and in particular, its relation to the Perron–Frobenius theorem. The MACS Graph Algorithm (MACSGA) is then coded for dynamic modelling purposes. Finally, the MACSGA is implemented on the vector borne disease network system to exhibit MACS’s effectiveness and reliability. It successfully identified the two districts that were the main sources of the outbreak based on their reproduction number, R 0 .

Suggested Citation

  • Nor Kamariah Kasmin & Tahir Ahmad & Amidora Idris & Siti Rahmah Awang & Mujahid Abdullahi, 2023. "Multidigraph Autocatalytic Set for Modelling Complex Systems," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:912-:d:1064730
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/912/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/912/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rika Preiser, 2019. "Identifying general trends and patterns in complex systems research: An overview of theoretical and practical implications," Systems Research and Behavioral Science, Wiley Blackwell, vol. 36(5), pages 706-714, September.
    2. Nurfarhana Hassan & Tahir Ahmad & Norhidayu M. Zain & Siti Rahmah Awang, 2020. "A Fuzzy Graph Based Chemometrics Method for Gelatin Authentication," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    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. Jessica Cockburn, 2022. "Knowledge integration in transdisciplinary sustainability science: Tools from applied critical realism," Sustainable Development, John Wiley & Sons, Ltd., vol. 30(2), pages 358-374, April.
    2. Christian Hoyer & Indra Gunawan & Carmen Haule Reaiche, 2020. "The Implementation of Industry 4.0 – A Systematic Literature Review of the Key Factors," Systems Research and Behavioral Science, Wiley Blackwell, vol. 37(4), pages 557-578, July.
    3. Jessica Cockburn & Eureta Rosenberg & Athina Copteros & Susanna Francina (Ancia) Cornelius & Notiswa Libala & Liz Metcalfe & Benjamin van der Waal, 2020. "A Relational Approach to Landscape Stewardship: Towards a New Perspective for Multi-Actor Collaboration," Land, MDPI, vol. 9(7), pages 1-20, July.
    4. Attila Soti, 2019. "Understanding Micro and Macro Interactions in Social Neurobiological Systems," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 17(4), pages 698-706.
    5. Samantha Papavasiliou & Carmen Reaiche & Shirley Papavasiliou, 2021. "Digital health and patient‐centred care: A digital systems view," Systems Research and Behavioral Science, Wiley Blackwell, vol. 38(2), pages 231-245, March.
    6. Nurfarhana Hassan & Tahir Ahmad & Naji Arafat Mahat & Hasmerya Maarof & Mujahid Abdullahi & Nur Farah Dina Ajid & Zarith Sofia Jasmi & Foo Keat How, 2023. "Authentication of Counterfeit Hundred Ringgit Malaysian Banknotes Using Fuzzy Graph Method," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    7. Marco Aurélio de Oliveira & Antonio Schalata Pacheco & André Hideto Futami & Luiz Veriano Oliveira Dalla Valentina & Carlos Alberto Flesch, 2023. "Self‐organizing maps and Bayesian networks in organizational modelling: A case study in innovation projects management," Systems Research and Behavioral Science, Wiley Blackwell, vol. 40(1), pages 61-87, January.
    8. João M. Lopes & Sofia Gomes & Lassana Mané, 2022. "Developing Knowledge of Supply Chain Resilience in Less-Developed Countries in the Pandemic Age," Logistics, MDPI, vol. 6(1), pages 1-19, January.

    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:gam:jmathe:v:11:y:2023:i:4:p:912-:d:1064730. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.