IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i1p151-d717758.html
   My bibliography  Save this article

How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach

Author

Listed:
  • Vicente Díaz-González

    (Doctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile
    These authors contributed equally to this work.)

  • Alejandro Rojas-Palma

    (Doctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile
    Departamento de Matemática, Física y Estadística, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile
    These authors contributed equally to this work.)

  • Marcos Carrasco-Benavides

    (Doctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, Chile
    Departamento de Ciencias Agrarias, Facultad de Ciencias Agrarias y Forestales, Universidad Católica del Maule, Curicó 3340000, Chile
    These authors contributed equally to this work.)

Abstract

This article presents a qualitative mathematical model to simulate the relationship between supplied water and plant growth. A novel aspect of the construction of this phenomenological model is the consideration of a structure of three phases: (1) The soil water availability, (2) the available water inside the plant for its growth, and (3) the plant size or amount of dry matter. From these phases and their interactions, a model based on a three-dimensional nonlinear dynamic system was proposed. The results obtained showed the existence of a single equilibrium point, global and exponentially stable. Additionally, considering the framework of the perturbation theory, this model was perturbed by incorporating irrigation to the available soil water, obtaining some stability results under different assumptions. Later through the control theory, it was demonstrated that the proposed system was controllable. Finally, a numerical simulation of the proposed model was carried out, to depict the soil water content and plant growth dynamic and its agreement with the results of the mathematical analysis. In addition, a specific calibration for field data from an experiment with wheat was considered, and these parameters were then used to test the proposed model, obtaining an error of about 6% in the soil water content estimation.

Suggested Citation

  • Vicente Díaz-González & Alejandro Rojas-Palma & Marcos Carrasco-Benavides, 2022. "How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach," Mathematics, MDPI, vol. 10(1), pages 1-19, January.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:151-:d:717758
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/151/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/1/151/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Araceli Queiruga-Dios & María Jesus Santos Sánchez & Fatih Yilmaz & Deolinda M. L. Dias Rasteiro & Jesús Martín-Vaquero & Víctor Gayoso Martínez, 2022. "Mathematics and Its Applications in Science and Engineering," Mathematics, MDPI, vol. 10(19), pages 1-2, September.

    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:10:y:2022:i:1:p:151-:d:717758. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.