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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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