Real realizations of algebraic differential equations

Many processes in natural sciences can be described by dynamical systems in the state-space form or, alternatively, by algebraic input-output equations. The question of recovering a dynamical system from a given input-output equation is known as the realizability problem. In this talk we give an overview of algebraic approaches to this problem when the dynamical system is restricted to have rational right-hand sides, and concentrate on finding realizations of input-output equations over the field of real numbers.