This course introduces modern mathematical modelling approaches using dynamical systems (largely differential equation approaches) that are relevant in many different applications and, in particular, for biological and ecological systems. In recent years, mathematical modelling has indeed become one of the most important research tools in biological research.

We will introduce the basic concepts and methods for analysis of linear differential equations and their intricacies under forcing and with resonances. This will lead to studying nonlinear dynamical systems taking advantage of applied bifurcation and chaos theory.

These tools will be used, in particular, to explore complex biological systems ranging from epidemics and infectious diseases (e.g., COVID), to the periodic processes driving the heart and brain or for studying ecological processes such as species persistence and biodiversity.

The assessment of this course will include implementing the techniques encountered in the lectures in a programming environment such as MATLAB.