Applied Problems of Nonlinear Oscillation and Wave Theory

The regime of the simultaneous existence of space and surface waves in the O-type oscillator with a periodically inhomogeneous comb has been considered. The impedance and quality factor dependences for space waves, surface waves and hybrid mode have been compared.

Effect of reflection from the remote load on the mode competition in a two-mode electronic maser is considered. A system of quasilinear equations for slowly varying amplitudes of the modes with cubic nonlinearity where the effect of reflections is taken into account by time delayed terms is analyzed. The most typical case of competition of two modes with close frequencies at the centre of generation zone is studied in detail. Change of generation regimes with increasing of reflections of the spurious mode at different values of delay is investigated analytically and numerically.

The effects of synchronization in the system of two coupled oscillators with delay are investigated. The picture of possible modes of generation in the case of identical and non-identical excitation parameters is studied in detail. The possibility of full synchro-nization in the stationary single-frequency, self-modulation and chaotic generation regime is demonstrated. The regime of «broadband synchronization» is found. In contrast with coupled finite dimensional systems, the boundaries of broadband synchronization area have wavy form.

Evolution of probabilistic distribution in self-sustained oscillators with increase of noise intensity is studied by means of numerical simulation and natural experiments. Two different systems are considered: van der Pol and Anishchenko–Astakhov self-sustained oscillators. Destruction of probabilistic distribution form, which is typical for noisy self-oscillation, by additive noise is showed.

This work presents results of experimental studies of coherence resonance phenomenon in UHF devices with long interaction (TWT and BWO). Basic properties of this phenomenon were investigated. Discovered suppression effect of resonant response on external noise by external harmonic signal. This suppression effect can be used to increase signal-to-noise ratio in system’s output. Specific features of coherence resonance phenomenon in long-interaction devices also noted.

One-parameter study of system of two nonlinearly coupled nonidentical Lang–Kobayshi oscillators is presented. The time delay influence on oscillation regimes in the system is studied. The posibility of periodic and quasiperiodic oscillations is shown. Variation of delay time leads to bifurcations and an alternation of periodic and quasiperiodic oscillations. Quasiperiodic oscillations are excited as a result of Neimark–Sacker bifurcation.

A numerical simulation of a wide band or secure communication scheme, based on nonlinear admixture of an information signal to the chaotic one, and on synchronization of the transmitter and receiver generators, manifesting hyperbolic chaos. Synchronization of the transmitter and receiver is provided by a strong unidirectional coupling between them. The study of the possibility of synchronization between subsystems and functionality of the communication scheme are presented.

The problem of the excitation of two coupled oscillators is discussed in the case of the simple subharmonic resonance between the external force and eigen-frequencies of the oscillators. The corresponded phase equation is obtained.

It is description of the way in which chemical environment of Briggs–Rauscher autooscillating reaction affects characteristics of oscillations. It has been ascertained that variations of the iodide complexes concentrations perhaps occurs due to increases of oxygen concentration in media and intermediate’s concentration fluctuation. Influence was investigated one of the basic natural oxidizing agent oxygen and it radical forms on autocooperative mechanisms of Briggs–Rauscher reaction.

Experimental studies of stationary distributions of the electric field intensity and the concentration of charge carriers in the Gunn diode have been provided by using near-field microwave microscope. The numerical computer calculation of these quantities based on the dependence of electrons mobility and diffusion coefficient on the electric field has been carried out. The existence of a multidomain mode of Gunn diodes has been found experimentally and confirmed theoretically.