L. V. Cherkesova

One of objects of research within the limits of the theory of nonlinear oscillations are laws and appropriateness of parametrical resonance in the higher zones of instability of oscillations. Researches on increase of speed and efficiency of modulation of parametrical systems go in several directions, but perspective direction in creation of electronic means of the future is elaboration of devices on the basis of the resonant schemes, working on the higher harmonics in the higher zones not-stability of oscillations. This question is insufficiently studied. In earlier published works devoted to this question were considered amplitude-and-frequency characteristics of the nonlinear resonator - nonlinear parametrical zone (pazone) system, working in I and II zones of parametrical excitation of oscillations, in a mode of the first and second resonances, that is only in the two first zones of instability of Matier. Interest is represented by researches of processes in the higher zones of instability of oscillations to which earlier it was not given sufficient attention. In offered article the general equations and formulas for the analysis of the nonlinear oscillatory systems functioning in any zone of parametrical excitation with number, where are received. It is established that nonlinear parametrical zone system can generate the higher harmonics at small enough attenuation. The system attenuation less, the more number of zones of excitation it is, and that raised oscillations have the big amplitude. The more strongly nonlinearity, the is more quantity of zones of excitation and the richer a choice of harmonics in which projected and designing devices on the basis of nonlinear parametrical zone systems can work. Analyzing the results received in article, it is possible to draw a conclusion that nonlinear parametrical zone system can generate the higher harmonics at small enough attenuation. The received amplitude parities and curves of dependences also are suitable for the analysis of oscillations in any zone of instability (excitation) with number n. It is shown that with other conditions being equal, in strongly nonlinear parametrical zone system (from the curve of magnetization close to rectangular), exists more number of zones of excitation of the higher harmonics, in which oscillations, than in weak nonlinear NPS (from not rectangular curve of magnetization) are possible. The attenuation of NPS is less, the more number of zones of excitation, in which oscillations (the more number of harmonics are possible can be excited) the raised oscillations (harmonic) have bigger amplitude. In strongly nonlinear system oscillation cease to be raised and disappear at attenuation more considerably, than in weak nonlinear NPS. The more strongly nonlinearity, the more zones of excitation and the richer a choice of harmonics in which the projected and designing device can work. Thus, the amplitude parities, received in given work and dependence for reception of amplitude and amplitude-frequency characteristics of NPS can be used at the analysis and designing of nonlinear oscillatory systems - parametrical generators and modulators, counting and logic units, etc. on the basis of nonlinear-parametrical zone systems, working in the higher zones of instability of oscillations.