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Topic and aim. The dynamics of a double-resonator gyroklystron of the 93 GHz band with delayed feedback is studied. A comparative analysis of the dynamical regimes of amplifier generation obtained in the numerical experiment both on the basis of averaged equations and in the framework of direct numerical simulation by the «particle-in-cells» method using the KARAT code is carried out. Method.

The method for controlling chaos in a ring resonator filled with a medium with cubic phase nonlinearity (Ikeda system), suggested in [1], is investigated within the framework of a distributed spatio-temporal model described by a Nonlinear Schr¨ odinger Equation with time-delayed boundary condition. Numerical results are presented which confirm the capability of the suggested method. For the case of weakly dispersive nonlinear medium, the results are in good agreement with the approximate theory based on the return map [1].

Method of controlling chaos in a ring cavity containing a media with cubic phase nonlinearity (Ikeda system) is considered. The proposed method is based on introduction of an additional feedback loop with parameters chosen so that the fundamental frequency components after passing through different feedback loops appear in phase, while the most unstable sidebands appear in antiphase, thus suppressing each other. In the weak dispersion limit a discrete map is derived that is a modification of the well-known Ikeda map.

Nonstationary theory of the reflex klystron oscillator based on differential equation with delay is developed. Analysis of self­excitation conditions, steady­state oscillation regimes and their stability is presented. Application of the developed theory for calculating of output characteristics of micromachined submillimetre­band reflex klystron is presented as well. Theoretical results are compared with the results of numerical simulation based on the particle­in­cell method.

A modified radio­electronic analog of the nonlinear ring cavity is realized in laboratory. The device represents a special class of oscillations or waves sources. An operation principle of the sources is based on interference amplification of feedback signal by an input signal. A laboratory experiments are performed, the likeness of their results and simulation data is shown. An intermittency, chaos, regular, static modes are detected. A thesis on controlled nonlinearity of dynamical systems is suggested.

The attempt is undertaken to define a class of oscillations or waves sources, the operation principle of which is based on interference amplification of feedback signal by an input signal. The precedent here is the optical Ikeda’s system. The radio­electronic analog of a nonlinear ring interferometer and it modification are offered, the block diagrams and mathematical models are constructed. The computer simulation is performed. An intermittency, chaos, regular, static modes are detected.

The 1.5 D code program of numerical simulation of nonlinear nonstationary processes in the klystron-type devices based on the nonstationary L.A. Vainshtein’s theory of cavity excitation and the «particle-in-cell» method for modeling of the electron beam dynamics is developed. The results of numerical simulation of the basic oscillation modes of the fourcavity klystron oscillator with the external delayed feedback are presented.