thumb|300px|Schematic representation of a self-oscillation as a positive feedback loop. The oscillator V produces a feedback signal B. The controller at R uses this signal to modulate the external power S that acts on the oscillator. If the power is modulated in phase with the oscillator's velocity, a negative damping is established and the oscillation grows until limited by nonlinearities.
Self-oscillation is the generation and maintenance of a periodic motion by a source of power that lacks any corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefore distinct from forced and parametric resonators, in which the power that sustains the motion must be modulated externally.
In linear systems, self-oscillation appears as an instability associated with a negative damping term, which causes small perturbations to grow exponentially in amplitude. This negative damping is due to a positive feedback between the oscillation and the modulation of the external source of power. The amplitude and waveform of steady self-oscillations are determined by the nonlinear characteristics of the system.
Self-oscillations are important in physics, engineering, biology, and economics.
History of the subject
The study of self-oscillators dates back to the early 1830s, with the work of Robert Willis and George Biddell Airy on the mechanism by which the vocal cords produce the human voice. Another instance of self-oscillation, associated with the unstable operation of centrifugal governors, was studied mathematically by James Clerk Maxwell in 1867. In the second edition of his treatise on The Theory of Sound, published in 1896, Lord Rayleigh considered various instances of mechanical and acoustic self-oscillations (which he called "maintained vibration") and offered a simple mathematical model for them.
The term "self-oscillation" (also translated as "auto-oscillation") was coined by the Soviet physicist Aleksandr Andronov, who studied them in the context of the mathematical theory of the structural stability of dynamical systems.