Прикладные задачи нелинейной теории колебаний и волн

In this letter we study nonlinear dynamics and transition to chaos in semiconductor superlattice coupled to external linear resonator. We have shown that such system demonstrates chaotic dynamics in wide range of supply voltage, whereas in autonomous superlattice only periodical dynamics exists. Revealed that transition to chaos in system goes through intermittency.

Experimental studies of stationary distributions of the electric ?eld intensity and the concentration of charge carriers in the Gunn diode have been provided by using near-?eld microwave microscope. The numerical computer calculation of these quantities based on the dependence of electrons mobility and di?usion coe?cient on the electric ?eld has been carried out. The existence of a multidomain mode of Gunn diodes has been found experimentally and con?rmed theoretically.

It is description of the way in which chemical environment of Briggs–Rauscher autooscillating reaction a?ects 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 ?uctuation. In?uence was investigated one of the basic natural oxidizing agent oxygen and it radical forms on autocooperative mechanisms of Briggs–Rauscher reaction.

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.

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.

One-parameter study of system of two nonlinearly coupled nonidentical Lang–Kobayshi oscillators is presented. The time delay in?uence 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.

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 e?ect of resonant response on external noise by external harmonic signal. This suppression e?ect can be used to increase signal-to-noise ratio in system’s output. Speci?c features of coherence resonance phenomenon in long-interaction devices also noted.

Evolution of probabilistic distribution in self-sustained oscillators with increase of noise intensity is studied by means of numerical simulation and natural experiments. Two di?erent 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.

The e?ects 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 ?nite dimensional systems, the boundaries of broadband synchronization area have wavy form.

E?ect of re?ection 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 e?ect of re?ections 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.