Engineering Physics Annotation << Back DYNAMICS OF PARAMETRIC INSTABILITY OF A LINEAR OSCILLATOR. EXACTLY SOLVABLE MODEL N.S. EROKHIN, V.E. ZAKHAROV The examples of exact solutions of mathematical models that describe the excitation of oscillations as a result of the development of parametric instability of a linear oscillator during the modulation of its frequency square. Considered exact solutions show a variety of regimes of parametric instability development and demonstrate the variants to control the processes of oscillations generation including a variable rate of the oscillator amplitude growth, the saturation of this instability at a given level of oscillation amplitudes, the possibility of a low-frequency modulation of instability increment i.e implementation of various scenarios of parametric instability development in the system considered. Keywords: Linear oscillator, square modulation of its frequency, parametric instability, parametric resonance, growth of oscillation amplitude, treatment of parametric instability, the amplitude gain of the oscillator, the exact solution, the saturation of the parametric instability, phase plane, singular point of type unstable focus, change the mode gain-attenuation regimes of the oscillator amplitude dynamic. Contacts: E-mail: nerokhin@mx.iki.rssi.ru, E-mail: zakharov@math.arizona.edu Pp. 36-40.