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За работы в области электромеханического моделирования флаттера Сергею Павловичу Стрелкову и Всеволоду Игоревичу Смыслову решением жюри конкурса имени профессора Н.Е. Жуковского от 2 января 1962 года присуждена премия первой степени за 1960 год.

The description of base concepts concerning to self-oscillations of nonconservative systems with asymmetrical couplings is given, in particular, such as the complex proper forms and frequencies, and complex normal coordinates.

We propose a dynamic system determined by a many-dimensional logistic map as a variant of a nonlinear model for dynamics of a biological many-group population. In some parts of a compact phase space the map displays a behavior which is atypical for a one-parameter one-dimensional logistic map. For a many-group population model it means stepwise changes of a total population density and densities of population age groups. We have an opportunity of getting a total population age groups changing periodically with the same period in many various parts of a phase space.

Investigation results of nonlinear dual-frequency model of resonance transmission line on backward volume magnetostatic waves are demonstrated. The system of two coupled oscillatory circuits is used as a model. The parameters of system depend on the input signal power level and on the detuning value between large and small signals. The results of the model are compared with the experimental data.

Through numerical simulation by nonlinear Schr¨ odinger equation magnetostatic wave soliton formation process is considered when amplitude and shape of initial pulse differ from soliton solution and non-soliton part can influence on soliton evolution. It is shown, that in lossless approximation soliton peak amplitude can oscillate with spatial period L: LD · L · 66 ¢ LD (or friequency W: 0:015 ¢ T¡1 D · W · T¡1 D ), LD и TD – length and time of dispersion.

The methods of sensitivity analysis of cycles under deterministic and stochastic disturbances for Higgins model describing glycolytic self-oscillations are considered. Two approaches connected with local exponents and stochastic sensitivity function are compared. The most sensitive parts of cycles are discovered. It was found that some parts of cycle lose stochastic stability along with stability increasing of cycle as whole.

In this paper, a comparative study of methods for classification of neuronal action potentials is performed, namely, the standard Principal Component Analysis (PCA) and techniques based on the wavelet-transform. It is shown that there are at least two caseswhen the wavelet-based approaches have advantages: 1) the presence of a small-scale structure in the shapes of spikes, and 2) the presence of slow noise of high intensity. It is stated that the quality of spike-sorting can be increased by signal’s filtering.

Scaling regularities are examined associated with effect of additive noise upon a critical circle map at the golden-mean winding number. On a basis of the RG approach of Hamm and Graham [1] we present an improved numerical estimate for the scaling constant responsible for the effect of noise, g = 2:3061852653::: Decrease of the noise amplitude by this number ensures possibility of observation for one more level of fractal-like structure associated with increase of characteristic time scale by factor (p5 + 1)=2.

We invetsigate mechanisms of appearance and disappearance of regimes of complete synchronization of chaos in a ring of three logistic maps with symmetric diffusive coupling. Two-parametric bifurcational analysis is carried out and typical oscillating regimes and transitions between them are considered.

Bifurcations in nonlinear systems with weak noise are considered. The local bifurcations are discussed: the saddle-node bifurcation, the transcritical bifurcation, the supercritical and subcritical pitchfork bifurcations. 

 Basing on the known prebifurcational noise rise and saturation phenomenon, the inverse problem is introduced: the problem of the bifurcation detection and determining it’s type by the observed noise change (noise deviation growth fashion, saturation level, probability density). The inverse problem solution algorithm is suggested.