# квазипериодическая динамика.

## COUPLED SELFSUSTAINED 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.

## PHASE DYNAMICS OF PERIODICALLY DRIVEN QUASIPERIODIC SELFVIBRATING OSCILLATORS

Synchronization phenomena are studied in phase dynamics approximation in the periodically driven system of two coupled oscillators. The cases are discussed when the autonomous oscillators demonstrate phase locking or beats with incommensurate frequencies. Lyapunov charts are presented, the possible regimes of dynamics of the driven system are discussed. Different types of twodimensional tori are revealed and classified.

## FORMATION AND BREAKDOWN OF A MULTILAYERED CLOSED CURVE IN NONINVERTIBLE MAPS

The paper describes the mechanism for the formation of closed invariant curves that are formed as layered structures of several sets of interlacing manifolds each with their associated stable or unstable resonance modes. Such invariant curves can arise, for instance, if the saddle cycle on a «simple resonance curves» undergoes perioddoubling or pitchfork bifurcations transversely to the circumference of the closed curve.

## 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.

## SYNCHRONIZATION OF REACTIVELY COUPLED PHASE OSCILLATORS DRIVEN BY EXTERNAL FORCE

Synchronization of two reactively coupled van der Pol oscillators with external force is investigated in this paper. We consider and compare quasi-periodic motion of oscillators with frequency-locked mode. The paper includes maps of Lyapunov’s exponents, two-parametric bifurcation diagrams and phase portraits. Possible types of motion in driven system are discussed.