-

The quantum dissipative system with quadratic potential confined by infinite walls of well and subjected to impulse pump was investigated in detail. The numerical simulation was carried out in context of the Schrodinger-Langevin-Kostin equation. The propagation of quantum wave packets, calculations of phase trajectories and mappings, dynamical averages, frequency spectra have been performed and discussed.

The synchronization by external periodic force of Lorenz system is under both numeric and analytical investigation in this paper. Properly studied the changes in synchronization caused by alteration of parameter value, which is responsible for arising of chaotic attractor in autonomous system.

Effective method of signals analysis based on the continuous wavelet transform is proposed in this paper. Application of this method to estimation of mean value both of laminar and turbulent phase durations corresponding to different types of intermittent behavior is considered including analysis of time series produced by living systems. It is shown that the proposed method is stable to noise and fluctuations distorting the initial time series.

The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems dynamics is proposed. The application of this method is illustrated by the consideration of the fluid model of Pierce diode which is one of the base system of plasma physics and of microwave electronics.

Spectra of oscillations in the system of two coupled self-sustained chaotic oscillators are investigated in present work. The relation between spectra and partial effective phase diffusion coefficients is determined. We follow the evolution of spectra and diffusion coefficients from the asynchronous regime to the regime of synchronous chaos. The analogy between spectral characteristics of coupled chaotic oscillators and noisy coupled periodic oscillators is drawn.

The particular properties of dynamics are discussed for the dissipatively coupled van der Pol oscillators, nonidentical in values of parameters controlling the Hopf bifurcation. The opportunity of a special synchronization regime in an infinitively long band between oscillation death and quasiperiodicity areas is shown for such system.

A mechanism of collective generation of bursts in ensembles of spiking neurons with nonlocal excitatory coupling is studied. Three types of the network topology is considered: (a) chains with regular short-range nonlocal coupling, (b) chains with a small number of random long-range connections and dominating regular short-range ones, (c) random ensembles with a power law of node degree distribution. It is shown, that there exists a common mechanism of burst generation resulting from instability of synchronous slow spiking as the coupling strengthens, giving rise to fast repetitive spikes.

The structure of the plane of period-doubling control parameters is discussed for the set of coupled differential systems proposed by J. Sprott. It is shown, that the behavior of these systems may be both similar to one of the popular coupled Ressler system and different from it.

The necessity of the considering the historical-geological and paleogeomorphological regularities of the river basin formation in the modeling of natural (river genesis) oil reservoirs structure has been discussed. River network developed at the different geological epochs can not represent the modern river network similarity. Therefore, formodeling the oil reservoirs structure it is necessary to take into account the possible structure differences between old and modern river networks.

We discuss the conception of the adaptive modeling of the natural oil reservoirs. This conception is based on application of simple mathematical algorithms to imitate the physical processes, defining the reservoir structure. As an example the possibility of fluvial reservoir modeling by a cellular automata is considered.