How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach
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...
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| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/1/151 |
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| author | Vicente Díaz-González Alejandro Rojas-Palma Marcos Carrasco-Benavides |
| author_facet | Vicente Díaz-González Alejandro Rojas-Palma Marcos Carrasco-Benavides |
| author_sort | Vicente Díaz-González |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:31:49Z |
| format | Article |
| id | doaj.art-62f6c06358a44d80aa04458c0c7ce6e0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:31:49Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-62f6c06358a44d80aa04458c0c7ce6e02023-11-23T11:54:55ZengMDPI AGMathematics2227-73902022-01-0110115110.3390/math10010151How Does Irrigation Affect Crop Growth? A Mathematical Modeling ApproachVicente Díaz-González0Alejandro Rojas-Palma1Marcos Carrasco-Benavides2Doctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, ChileDoctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, ChileDoctorado en Modelamiento Matemático Aplicado, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca 3460000, ChileThis 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.https://www.mdpi.com/2227-7390/10/1/151nonlinear systemsstabilitycontrollabilityirrigation strategysoil–plant- atmosphere continuum |
| spellingShingle | Vicente Díaz-González Alejandro Rojas-Palma Marcos Carrasco-Benavides How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach Mathematics nonlinear systems stability controllability irrigation strategy soil–plant- atmosphere continuum |
| title | How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach |
| title_full | How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach |
| title_fullStr | How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach |
| title_full_unstemmed | How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach |
| title_short | How Does Irrigation Affect Crop Growth? A Mathematical Modeling Approach |
| title_sort | how does irrigation affect crop growth a mathematical modeling approach |
| topic | nonlinear systems stability controllability irrigation strategy soil–plant- atmosphere continuum |
| url | https://www.mdpi.com/2227-7390/10/1/151 |
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