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

Coupled oscillators

Dynamics of three coupled van der Pol oscillators with non-identical controlling parameters

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.

The research of excited by external signal system of two coupled van der Pol oscillators at transition to the regime of amplitude death in the autonomous system

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.

Revealing nonlinear couplings between stochastic oscillators from time series

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.

Hyperbolic chaos in a system of nonlinear coupled Landau-Stuart oscillators

Chaotic dynamics of a system of four nonlinear coupled non-identical LandauStuart oscillators is considered. Subsystems are activated alternately by pairs due to a slow 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 Poincare section depending of coupling. Some systems with different type of coupling corresponded to «maximum» and «minimum» chaos are investigated. 

Coupled self-­sustained oscillators of different nature by example of van der Pol system and brusselator

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.

Study of synchronization in the system of two delay-coupled gyrotrons using a modified quasilinear model

Topic. The paper is devoted to the study of mutual synchronization of two gyrotrons coupled with delay. As a rule, a theoretical study of synchronization of gyrotrons and other microwave oscillators is usually carried out by numerical simulations using certain well-established models of microwave electronics. Using this approach, it is difficult to provide a fairly complete synchronization pattern, using methods and ideas of nonlinear dynamics. Aim.