Podgajko O. Mathematical models of asymmetric nonlinear systems in maximum zones of instability of oscillations

Object - nonlinear oscillations in zones of parametrical instability. The aim - development of methods and means of research of parametrical oscillations in the resonances system at external influence, construction of mathematical models of asymmetric nonlinear system with fading and development of experimental means of research. Methods - methods of the theory of nonlinear oscillations and theory of the nonlinear differential equations with periodic coefficients. Results - spread of knowledge about the parametrical phenomena in the resonances systems at external influence and occurrence of oscillations of the maximum zones instability, definition character of influence not identity parameters of elements on amplitude-frequency characteristic of system, increase of exactness for the description of physical processes in nonlinear systems. The mathematical models take into account energy parities in asymmetric system, link amplitude and a phase of oscillations of system in an any zone of parametrical excitation with the parameters of influence, allow to describe physical and other systems at external influence. The developed modeling means and the received expressions enable to estimate modes of operation of created devices on the basis of inductive nonlinear parametrical systems. Implementation - three research works KNURE (520-10, 108-3, 162-3), a design department of enterprise "Projector" (Malin), educational process of faculty "Designing and operation of electronic devices" (KNURE)