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


Estimation of interaction direction between oscillatory model systems in case of close coupling

The task of detection statistically signi?cant interaction, its direction and delay between time data series of two oscillatory systems in case of close coupling is investigated with nonlinear modeling approach. Numerical experiments on oscillatory model systems with di?erent coupling function variants are used to study main dependences.

Effect of rare sampling on estimation of directional couplings from time series

The problem of detection and quantitative estimation of directional couplings (mutual in?uences) between systems from discrete records of their oscillations (time series) arises in di?erent ?elds of research. This work shows that results of the traditional «Granger causality» approach depend essentially on a sampling interval (a time step). We have revealed the causes and character of the in?uence of a sampling interval on numerical values of coupling estimates.

Influence of the choice of the model structure for working capacity of nonlinear granger causality approach

Currently, the method of nonlinear Granger causality is actively used in many applications in medicine, biology, physics, to identify the coupling between objects from the records of their oscillations (time series) using forecasting models. In this paper the impact of choosing the model structure on the method performance is investigated. The possibility of obtaining reliable estimates of coupling is numerically demonstrated, even if the structure of the constructed forecasting model differs from that of the reference system.

On the period-multiplying bifurcation of glacial cycles in the pliocene – pleistocene

In the Pliocene (about ?ve – two million years before present) global climate ?uctuated with a period corresponding well 41-thousand-year cycle of changes in the Earth’s axis inclination to the ecliptic plane. Then, this period has disappeared, despite the fact that the 41-thousand-year cycle even slightly increased its scope and, therefore, the response to it would have only strengthened. By analyzing paleoclimatic series covering the Pliocene and subsequent Pleistocene, we show that the response of the climate system simply became unstable and therefore unobservable.

Bifurcations in van der pol oscillator with a hard excitation in a presence of parametrical noise: quasi-harmonic analyzes and the numerical simulations

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.

«oscillator death» and quasiperiodic bifurcations in low- dimensional ensemble of van der pol oscillators

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.

New type of bifurcations in the modified rayleigh–benard ? convection problem

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.

System of three non-autonomous oscillators with hyperbolic chaos chapter 2 the model with da-attractor

  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.

Investigation of regular and chaotic dynamics of one financial system

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.

Spiral structures from heavy particles at parametrical excitement of standing capillary waves

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.


Умер Дмитрий Иванович Трубецков. Прощание состоится 14 августа в 11.30 в Актовом зале 10 корпуса СГУ.