Applied Problems of Nonlinear Oscillation and Wave Theory

There was conducted the research of comparative physiological assessment in nonlinear analysis methods of heart rate variability (HRV): the approximate entropy (ApEn), sample entropy (SampEn), multiscale entropy (MSE) and detrended fluctuation analysis (DFA) in case of remote ischemic preconditioning (RIPC) and orthostatic test both in healthy young subjects and individuals with autonomic regulation imbalance.

Предложен способ построения одномерного отображения с заданной плотностью распределения случайной величины (инвариантной мерой) и заданной корреляционной функцией (временем корреляции). Указанная процедура может оказаться полезной в тех приложениях, где приходится моделировать псевдослучайные процессы с заданными свойствами или сопоставлять сложному случайному процессу более простой (одномернсе отображение), совпадающий с ним по ряду параметров.

Предлагается критерий возникновения хаотической динамики при слабонелинейном взаимодействии волн. При этом обобщается критерий возникновения хаоса при взаимодействии типа волна - частица. Роль ширины нелинейного резонанса играет инкремент неустойчивости. Численный анализ подтверждает этот критерий.

Описываются результаты расчетов размерностей и поиска периодических траекторий по временным рядам метеорологических данных, рассматриваемых как реализации траекторий хаотической динамической системы.

Using the functional reflection method the nonlinear dynamics of the TWT­generator with delayed feedback is considered. It is shown, that if the feedback factor is small, the region of linear stage beam-wave interaction assumes a character of narrow-band filter. So, the quasi-monochromatic signal is formed to the begining of the nonlinear stage of interaction. The resonance character of the beam instability leads to the strong dependence of the field dynamics on the instantaneous signal freguency.

Purpose. To compare effeciency of different realizations of approaches to estimation of mutual information function based on nearest neighbours.

Method. Two approaches to calculation of mutual information function were realized numerically: straightforward approach is based on brute force, and sorting based one.

A new method is proposed in which constructing exact solutions to nonlinear evolution equations is based on successive applying the perturbation method and apparatus of the continued fractions. It is shown that exact solitary-wave solutions arise in the limiting case as the sum of geometric series of the perturbation method based on the linearized problem.

Mathieu quantum oscillator as a generalization of the classical one with cubic force, friction and noise has been proposed. The problem of the transition from classical to quantum behavior is of importance not only for fundamental knowledge but also for applications. As an example one can mention the oscillatory motion of low mass objects at decreasing temperature.

The work is devoted to investigation of multistability of running waves in a ring of periodic oscillators with diffusive non-local couplings. It analyzes the influence of long-range couplings and their change with distance on the stability of spatially-periodic regimes with different wave numbers.

Purpose. To suggest a new approach to reconstruction of couping architecture and individual parameters of first-order time-delayed oscillators from experimental series of their oscillations.