Self-oscillations are a phenomenon in physics and mechanics: self-sustaining periodic or quasi-periodic oscillations in a nonlinear system that, without periodic external forcing, maintains them by means of its own source of energy. The theoretical basis for describing self-oscillations was laid by the Nizhny Novgorod physicist Aleksandr Aleksandrovich Andronov, who created a mathematical apparatus that makes it possible to rigorously distinguish the self-oscillating regime from free and forced oscillations.
Physical nature and mathematical description
The distinguishing feature of a self-oscillating system is a stable limit cycle on the phase portrait: trajectories starting from different initial conditions are attracted to a closed curve that describes a steady, undamped oscillation. The classic model example is the van der Pol oscillator, an equation with nonlinear damping that provides self-pumping of energy at small amplitudes and limits it at large ones.
Modern research considers more complex regimes: quasi-periodic oscillations (motion along an invariant torus in phase space) and chaotic ones. Under adaptive external forcing, where the phase of the forcing additionally depends on a dynamical variable of the oscillator, one observes a widening of the subharmonic resonance tongues, the dominance of three-frequency tori, and the possible development of hyperchaos as a result of the breakdown of a two-frequency torus.[1]
Self-oscillations in technical applications
Self-oscillating regimes arise not only in radiophysical generators but also in superconducting devices. In particular, studies from 2024 are devoted to a theoretical analysis of self-oscillations in an RFTES bolometer (a superconducting film microbridge incorporated into a high-Q resonator): models of competition between the heating current and the critical current were considered, as well as the formation of a hot spot upon local breakdown of superconductivity; the simulation results qualitatively confirmed the experimental data.[2]
The Nizhny Novgorod connection
The concept of "self-oscillations" as an independent physical term was introduced into science by Aleksandr Aleksandrovich Andronov, who worked in Nizhny Novgorod. It was he who showed, in the late 1920s, that periodic processes in radio-engineering generators differ fundamentally from free damped and forced oscillations and must be described by Poincaré's theory of limit cycles. The Nizhny Novgorod (Gorky) scientific school of nonlinear oscillations, which grew up around Andronov, remained for decades the world's leading center for the theory of self-oscillating systems.
Sources
- cyberleninka.ru — SELF-OSCILLATING SYSTEMS WITH A CONTROLLED PHASE OF EXTERNAL FORCING
- mathnet.ru — L. S. Solomatov, A. V. Merenkov, S. V. Shitov, "Theoretical study of self-oscillations in an RFTES detector," Physics of the Solid State, 66:6 (2024), 836—842