Throughout the history of dynamical systems, instruments have been used to calculate and visualize (approximate) solutions of differential equations. Here we describe the approach of a group of physicists and engineers in the period 1948–1964, and we give ex- amples of the specific (analogue) mathematical in- struments they conceived and used. These examples also illustrate how their analogue culture and practices faced the advent of the digital computer, which appeared at that time as a new instrument, full of promises.