E. V. Kal’yanov

Autoparametric delay system with time lag

A new model describing a delay generator with time lag, which contains a filtering element, is proposed. The results of numerical analysis are considered. A modification of the model, in which autoparametric self-action is ensured in addition to a nonlinear retrieving force supplemented to the oscillatory circuit, is analyzed. It is shown that the autoparametric feedback in the modified model ensures excitation of developed chaos with a broad power spectrum even in the case of weak nonlinearity.

Data transmission through a radio channel using masking oscillations

A scheme of data transmission through a radio channel masked by chaotic oscillations is considered. A mathematical model describing the system is formulated in the case of chaotic oscillations generated in two separated frequency bands. The results of a numerical analysis of the model are presented. It is demonstrated that hidden data transmission in such a channel is possible.

Mutual chaotic synchronization of self-oscillating systems with inertance in a noise-like environment

The effect of external chaotic oscillations on systems of coupled generators with chaotic dynamics is studied. Coupled self-oscillating systems, in which partial generators are characterized either by Lorentz equations or by Rössler equations presented in the form of subsystems with inertance, are used as examples. The case of identical external chaotic oscillations affecting partial generators is considered. It is demonstrated that the synchronism of interacting oscillations is enhanced for both Lorentz andRössler coupled oscillations if the influences of noise-like oscillations on partial generators are identical.

Transient processes under stochastic synchronization of oscillators in colored-noise medium

Equations that describe mutual and induced chaotic synchronization of n (n = 2, 3, 4,...) autooscillation systems in colored-noise medium are derived. It is demonstrated that external colored noise acting upon a system of coupled oscillators and a chain of unidirectionally coupled oscillators causes a decrease in the duration of transient processes that lead to the chaotic synchronization (both mutual and induced) of nonidentical oscillators and a decrease in the time needed for stabilization of the symmetric state of the system when the parameters of oscillators are identical.

Mutual chaotic synchronization of self-oscillating systems in a noisy environment

The equations that describe mutual chaotic synchronization of self-oscillating systems in a noisy environment are analyzed. The solutions of equations with chaotic dynamics and the RND code that produces external noise with normal distribution law are used as the sources of external oscillations. It is demonstrated that, in contrast to the expected effect of deterioration of mutual synchronization, synchronism of interacting chaotic oscillations is improved as the external noise-like action gets stronger in both cases of the influence of irregular oscillations on partial generators.

Effect of colored noise on chains of chaotic oscillators

Equations that describe a ring system consisting of a closed circuit of n (n = 2, 3, 4, ...) unidirectionally coupled self-oscillation systems that exhibit chaotic dynamics are analyzed in the presence of external colored noise. For simplicity, detailed results of numerical calculations are presented for three oscillators. It is demonstrated that the external colored noise that is exerted upon partial oscillators of the ring system may facilitate the development of synchronous oscillations and reduce transient processes related to stabilization of chaotic synchronization. The effect is qualitatively interpreted. For comparison, numerical methods are employed to analyze the effect of external colored noise on an open circuit consisting of three oscillators.

Chaotic oscillations in a coupled system of bistable oscillators

The influence of the asymmetry of the nonlinear element characteristic on the chaotic oscillations of Chua’s bistable oscillator is studied. It is shown that such asymmetry causes asymmetry of a chaotic attractor that maps the switching of motions between two basins of attraction up to the concentration of oscillations in one basin. Oscillation control in a bistable chaotic self-oscillating system (two coupled Chua’s oscillators) is considered. It is demonstrated that oscillations excited in two basins of attraction may pass to one of them and that oscillations may build up in two basins when they are autonomously excited in different basins. It is also found that chaotic oscillations in a coupled system may be excited at parameter values for which the autonomous chaotic oscillations of partial oscillators are absent. The influence of external noiselike oscillations is investigated.

Mutual synchronization in a system of two bistable oscillators executing regular and chaotic oscillations

A numerical analysis of a new model describing two coupled modified Chua’s oscillators is conducted. Equations of a partial oscillator differ from classical equations in that the former contain additional delayed feedback in another writing of dimensionless time. Changeover from regular oscillations in the absence of additional feedback to additional-feedback-induced (switchable) chaotic oscillations is studied. It is shown that, when normal regular oscillations, as well as additional-feedback-induced chaotic oscillations, are synchronized, difference oscillations are left. They are absent only when the control parameters of partial oscillators are identical. The application of a harmonic signal allows one to control the oscillations of a chaotic system of coupled modified bistable oscillators.

Locking of self-oscillatory systems with random dynamics

Equations are proposed for describing a self-oscillatory system with a time delay and random dynamics. The interaction of two such systems with mutual diffusion-controlled coupling and the case of one-way coupling are analyzed. It is shown that in both cases, the locking is partial because difference random oscillations persist. Transient processes in random locking stabilization are considered

Self-sustained oscillations in systems with delay under irregularly varying excitation conditions

A mathematical model of a system consisting of two coupled chaotic delay subsystems is presented. Instead of constant initial conditions in the form of a single impetus to excite the subsystems, continuous irregular oscillations are used that simulate intrinsic noise and continue acting on self-sustained oscillations after their excitation. An equation of an autonomous subsystem with regard to feedback variation is derived. It is shown that, when an autonomous subsystem is excited by irregular oscillations, chaotic motions become stochastic. In this case, the intensity of oscillations simulating intrinsic noise increases, suppressing self-sustained oscillations and providing the regenerative amplification of irregular oscillations. Interaction of coupled oscillations for identical and nonidentical subsystems is considered for the case of different noiselike initial conditions. It is found that interacting oscillations are not completely identical even if the parameters of the subsystems are the same.