Связанные осцилляторы

Problem of interaction between self­sustained oscillating systems of different nature is discussed by an example of coupled brusselator and van der Pol oscillator. Picture of leading oscillator changing with the growth of coupling parameter is shown. Areas of different types of dynamics are indicated in the parameter space. The case of essentially different eigenfrequencies is discussed.

Chaotic dynamics of a system of four nonlinear coupled non-identical Landau-Stuart oscillators is considered. Subsystems are activated alternately by pairs due to aslow variation of their parameters responsible for the Andronov–Hopf bifurcation. It is shown, that system dynamics depends of coupling type. Different types of phase map (Bernoulli type map) are obtained in Poincar´ e section depending of coupling. Some systems with different type of coupling corresponded to «maximum» and «minimum» chaos are investigated.

One of the key turbulence theory idea is a cascade energy transmission through the spectrum from large to small scales. It appears that this idea could be used for complex dynamics realization in a different­nature systems even when equations are knowingly differ from hydrodynamical. The system of four van der Pol oscillators is considered in this paper. Chaos generation is realized by cascade excitation transmission from one oscillator to another with frequency doubling.

The problem of detection and quantitative characterization of nonlinear directional couplings between stochastic oscillators is considered. Coupling characteristics and a technique for their estimation from time series are suggested. An analytic expression for a statistical significance level of the conclusion about coupling presence is derived that allows a reliable inference from relatively short signals. Performance of the approach is demonstrated in numerical experiments with diverse individual properties of oscillators and different kinds of coupling functions.

We consider the chain of three dissipatively coupled self-oscillating systems with non-identical controlling parameters. We observe situations, when coupling damps different oscillators. The structure of the frequency mismatch – coupling value parameter plane is investigated with a view to the location of oscillator death area, complete synchronization area, two- and three-frequency quasiperiodic regimes. Features, connected with non-identity in controlling parameters, are considered.

Pulsed driven system of two coupled van der Pol oscillators in the regime of synchronization 1:1 and «oscillator death» is researched. The existence of islands of quasi-periodic regimes on the parameter plane period – amplitude of perturbation in the radiophysics experiment are shown. The different types of oscillations in this system are illustrated.