Mathematical modeling of fruit trees’ growth under scarce watering

Abstract

As a consequence of the Global Warming, the decrease in water resources is a problem that affects the agricultural systems worldwide. In particular, the Global Warming has produced a sustained decrease in precipitation in Mediterranean-type climatic zones and the more frequent presence of droughts. A dry-and hot environment could negatively affect the physiology of the fruit tree, compromising its growth and development rates, especially, the yield of a fruit tree results from the interactions between genotype, climate, soil, crop management, and irrigation. This work theoretically studies the growth dynamics of fruit trees with a limited water resource by a mathematical model. A system of non-linear ordinary differential equations was used as a method to describe the growing phenomenon. A qualitative analysis of the system was carried out, and local and global stability results were obtained. The analysis showed that the limitation of water resources compromises the growth dynamics of the fruit tree, causing a total loss of the fruit tree.