Differential Equations are the language used to describe processes in Science and Engineering. The understanding of these processes always begins with a first phase of description that is often followed by a second phase of mathematical modelling using Differential Equations. Going from the classical problem of the movement of the planets around the sun, to the study of the deformation of structures; from the analysis of the growth of complex nets like Internet to the study of the dynamics of the not less complex metabolic and genetic regulation nets. All these cases are modelled by Differential Equations.
Two of the main goals of the research of the Group of Differential Equations, Modelling and Applications at the Department of Computer Science and Applied Mathematics at the University of Girona are the derivation and analysis of new equations that describe biological processes (dynamics of populations, spread of epidemic diseases in complex networks) and processes of engineering (optimal design of transport networks), together with the study of the behaviour of the solutions of known differential equations of other fields, like for example, celestial mechanics.
The main research lines of the group are the following: complex networks, dynamics of structured populations, celestial mechanics, discrete dynamical systems, and some applications of differential equations