Can the drinking bird explain economic cycles? A history of auto-oscillations and limit cycles

摘要

The aim of this work is to sketch and, sometimes, to refine thehistory of the notion of self-sustained oscillations or auto-oscilla--tions in science and technology, and that of the mathematicalconcept of limit cycle of a system of ordinary differential equations.Devices producing self-sustained oscillations, i.e. able totransform a continuous source of energy into a periodic motionexist since Antiquity, and the most ludic one can be the drinkingbird, a scientific toy patented by an American inventor in 1946.Those self-sustained oscillations are of the greatest importance inclock-making, musical instruments, wireless telegraphy, frictiondynamics, chemistry, biology and many other fields.