-

In the work the behavior of a van der Pol oscillator with a hard excitation is considered near the excitation threshold under parametrical (multiplicative) Gaussian white noise disturbances, and in a case of the two noise sources presence: parametrical one and additive noise. The evolution of probability distribution is studied when a control parameter and a noise intensity are changed. A comparison of the theoretical results, obtained in the quasi-harmonic approach with the results  of numerical solutions of the oscillator stochastic equations is ful?lled.

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The e?ect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasi-periodic saddle-node and Hopf bifurcations.

The original Rayleigh–Benard convection is a standard example of the system where bifurcations occur with changing of a control parameter. In this paper we consider the modi?ed Rayleigh–Benard convection problem including radiative e?ects as well as gas sources on a surface. Such formulation leads to the identi?cation of new type of bifurcations in the problem besides the well-known Benard cells.

  We consider a system of three coupled non-autonomous van der Pol oscillators, in which the behavior of the phases over a characteridtic period is described approximately by the Fibonacci map with modi?cation of the «Smale surgery», which leads to the appearance of DA-attractor («Derived from Anosov»). According to the numerical results, the attractor of the stroboscopic map is placed approximately on a two-dimensional torus embedded in the six-dimensional phase space and has transverse Cantor-like structure typical for this kind of attractrors.

Based on complex numerical investigation for the nonlinear ?nancial system introduced by Chen a map of dynamic regimes has been built, depending on the bifurcation parameters. All the major scenarios of transition to deterministic chaos have been found. Theorems of the existence of the globally exponentially attractive set and positive invariant, of periodic solutions, of Poincare–Andronov–Hopf bifurcation existence and theorems in the ?eld of control of attractors are proved.

We study synchronization in ensembles of locally di?usive coupled Bonhoe?er–van der Pol oscillators. Individual elements frequencies in?uence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this e?ect are numerical modeling data and analytical research.

The paper presents experimental studies on the formation of spiral structures of heavy particles by the ?eld of parametrically excited standing spiral waves. Particles move under the in?uence of the average currents ?eld generated near the bottom in a viscous liquid by standing waves. The formation of structures has a threshold character and depends on the intensity of the ?eld of standing waves. Formation of multi-armed structures revealed.

Memory notes about childhood at the time of the Great Patriotic war.

Investigation and development of e?cient electromagnetic oscillations sources are one of the topical issues in the ?eld of terahertz radiophysics and electronics. A frequency region is regarded as an explored for which oscillating, amplifying and measurement devices have not been developed. The exploration of the terahertz frequency range is at the initial state.

Some results of researches and development of devices with ?eld emission (TWT, BWO, carcinotrode, klystrons and X-ray tubes, ?eld emission displays, etc.) have been brie?y presented in the article. Lines of development of its theory have been designated. Also the vacuum microwave electronics programs o?ered in Europe and USA have been considered. They are directed on using new technologies in coping with the terahertz frequency range, re?ecting the trend of recent years.