Abstract

I take the phrase ''the theory of nonlinear oscillations'' to identify a historical phenomenon. Under this heading a powerful school in Soviet science, L. I. Mandelstam's school, developed its version of what was later called ''nonlinear dynamics''. The theory of nonlinear oscillations was formed around the concept of self-oscillations, which was elaborated by Mandelstam's graduate student A. A. Andronov. This concept determined the paradigm of the theory of nonlinear oscillations as well as its ideology, that is, a set of characteristic ideas which, together with the corresponding examples and analogues, allowed the expansion of the theory into associated areas where it indicated new interesting phenomena and posed new problems. It was the ideology that made possible the broader application of the theory of nonlinear oscillations, whose domain was originally lumped systems, to continuous media and its subsequent progress toward synergetics. In the course of its ideological application, the concept of self-oscillations was greatly extended, became vague and diffuse, and related concepts such as self-waves and self-structures appeared.