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

Applied Problems of Nonlinear Oscillation and Wave Theory

Bifurcations of attracting sets of deformation displacement of cutting tool depending on the spindle group beats

Subject of the study. The bifurcations of the attracting sets of the deformational displacement of the tool in the dynamic system of the turning machine depending on the beats periodic trajectory of the spindle group are considered in the article. The dynamic system is represented by the two interact mechanical subsystems through the dynamic link formed by the cutting process. Through the link is represented by the forces model in the coordinate condition, the trajectories of the executive elements and the trajectories of the spindle beats group.

Chaos and order in athmospheric dynamics part 2. Interannual rhythms of the El Nino – southern oscillation

Processes of the El Nino – Southern Oscillation (ENSO) are investigated based on the mathematical theory of the so-called the strange nonchaotic attractor (SNA) in the quasiperiodically forced dynamic systems, and using the sea surface temperature and the atmospheric sea-level pressure data for the 1870–2014 year period. It is found that ENSO is influenced not only by the annual Sun-induced periodic heating of the climate system, but also by the three more other external forces which periods are incommensurable to the annual period.

Determining of the intermittent phase synchronization degree from neurophysiological

In this paper we present the results of investigation of intermittent phase synchronization in a real neurophysiological system. This phenomenon is observed in different systems as well as near the boundaries of various types of chaotic synchronization. In the case of electroencephalogram (EEG) of the brain, chosen as a system under study, just the intermittent phase synchronization can indicate the existence and development of pathologies, for example, the presence of epileptic seizures.

The effect of symmetry breaking on reversible systems with myxed dynamics

Theme – the effect of symmetry violation on the structure of the phase space of invertible systems. Aim – to study the changes in the phase space structure of invertible systems caused by the violation of symmetry, in particular, the possibility of multistability and the types of coexisting attractors. The peculiarities in comparison with the similar regimes in the systems with fixed constant dissipation also studied.

Asymptotic research of local dynamics of the Cahn–Hilliard family equations

Topic. Dynamics of well-known Cahn–Hilliard nonlinear equation is researched. In a state of balance stability task, critical cases were highlighted and bifurcation phenomena were researched. Aim. To formulate finite-dimensional and special infinite-dimensional equations, which can be represented as normal forms. Method. You can use as standard local dynamics research methods, based on constructing of normal forms on central manifolds, and special infinite-dimensional normalization ones.

On the question accounting of the resistance force at the hinge point of setting physical pendulum and its influence on the dynamics of movement

Topic. The paper is devoted to the analysis of the dynamics of a complex system, i.e. a hinge mechanism plus a compound pendulum, in which where a differential equation is found, describing its nonlinear behavior. Aim. The paper is in the analysis of nonlinear oscillations of a complex dynamical system, which is a hinge, a rod and a ball, setting together in the one way. It is assumed to obtain differential equation of motion of the pendulum with regard to the gimbal friction and the resistance of the continuum. Method.

Dynamics of coupled generators of quasi-periodic oscillations with equilibrium state

Subject of the study. Recently, the problems of synchronization of systems demonstrating quasi-periodic oscillations arouse interest. In particular, it can be generators of quasi-periodic oscillations that allow a radiophysical realization. In this paper we consider the dynamics of two coupled oscillators of quasi-periodic oscillations with a single equilibrium state. Novelty.

Synchronization self-sustained oscillators interacting through the memristor

Aim. The aim of the paper is to study the mutual synchronization of two periodic selfsustained oscillators with a detuning of frequencies interacting through a memristor. It is supposed to give an answer to the question of the possibility of synchronization in this case and of its probable features. Method. The study is carried out by methods of theoretical analysis and computer simulation of oscillations in a system of two van der Pol oscillators interacting through a memristive conductivity. As the latter, an idealized Chua memristor is used. Results.

Multistability of periodic orbits in ensembles of maps with long-range couplings

Aim. The aim of the investigation is to study the regularities of phase multistability in an ensemble of oscillatory systems with non-local couplings in dependance of strength and radius of the couplings, as well as to describe them from the point of view of the spatial spectrum. Method. Study has been carried out by means of numerical simulation of ensemble of logistic maps, by calculation of the phase differences between the oscillations in the subsystems, which define spatial phase clusters and analyze their spectra.

Multistability of traveling waves in an ensemble of harmonic oscillators with long-range couplings

The work is devoted to study of multistability of traveling waves in a ring of harmonic oscillators with a linear non-local couplings. It analyses the influence of the strength and radius of the couplings on stability of spatially periodic regimes with different values of their wavelengths. The system under study is an array of identical van der Pol generators in the approximation of quasi-harmonic oscillations.