Abstract

Physics continues to be an inexhaustible source of problems that have inspired the theoretical development of mathematics, particularly in the development of the theory of dynamical systems that have their origin in the physics of the 15th century, with the beginning of differential calculus by Newton and Leibniz; differential equations are an appropriate tool for research in different areas of knowledge. Our objective is to show an example of how we can use dynamical systems in a problem framed in forestry and agricultural systems, ecology, and epidemiology. This work is inspired by one of the essential primary crops in the energy intake of the human diet, wheat; as it turns out, the productivity of this food can be affected by several biotic stresses, including viral diseases and their associated vectors. Among the viral infections is the barley yellow dwarf virus, which causes 11% to 33% yield losses in wheat fields; the virus moves through the agricultural landscape via different aphid species (vectors). The main problem is that aphids prefer colonizing plants with the virus, causing rapid growth of infected plants and substantially decreasing crop productivity; therefore, we propose to study the dynamics of aphid-plant interaction, in which the impact of aphid preference for infected plants is determined, and we obtained as a result that a key parameter is the quantity and quality of food consumed by aphids.