ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Applied Problems of Nonlinear Oscillation and Wave Theory

Investigation of stability of nonlinear normal modes in electrical lattices

The problems of existence and stability of the symmetry-induced nonlinear normal modes in the electric chain of non-linear capacitors, connected to each other with linear inductors (the model described in Physica D238 (2009) 1228) are investigated. For all modes of this type, the upper limit of the stability region (in amplitude of voltage oscillations on capacitors) as a function of the chain cell number were found. Asymptotic formulas were determined at cell number tends to infinity.

Random distant couplings influence to a system with phase multistability

We explore the destruction of phase multistability which takes place in an ensemble of period doubling oscillators under the action of long-distance couplings, which appear randomly between the arbitrary cells. The investigation is carried out on the example of a chain of Rossler’s oscillators with periodic boundary conditions, where alongside with local couplings between the elements exist long-range interconnections. The sequence of bifurcations, which accompany increasing of the strength of the global coupling is determined.

Autooscillations in o-type oscillator at excitation of space-surface mode in resonator with a periodically inhomogeneous grating

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 delayed reflection from the remote load on mode competition in а gyrotron

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.

Mutual synchronization of two coupled generators with delay

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 synchronization 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.

Experimental research of self-oscillation destruction under additive noise action

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 selfoscillation, by additive noise is showed.

Coherence resonance in uhf devices with long interaction

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-tonoise ratio in system’s output. Specific features of coherence resonance phenomenon in long-interaction devices also noted.

Dynamics of two nonlinearly coupled nonidentical Lang–Kobayshi oscillators

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.

The study of the unidirectionally coupled generators of robust chaos and wide band communication scheme based on its synchronization

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.

Subharmonic resonance in a system of two dissipative coupled van der Pol oscillators with external force

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. We showed that the form of the synchronization tongue and transformation of the region of the two-, three-frequency tori by varying the parameter of the coupling between the oscillators is significantly different from the case of the main resonance.