Computing with analog models. Computing with ordinary differential equations

Differential equations is some universal language in many contexts, and in particular in experimental sciences. Motivated initially by analog models of computation, we will review various results demonstrating that it is possible to program with ordinary differential equations, or their discrete counterpart, discrete differences. We will show that several concepts from computability and complexity theory can be formulated in this framework. We will hence present some applications to bioinformatics, computer algebra, or logic.