Autowaves. Self-organization

The processes of oscillatory pattern formation in autooscillatory neuronal models are investigated. Such patterns play a key role in the information processes used in higher brain functions. The effect of pulse-induced phase autoreset in the model of neurons with subthreshold oscillations is studied. As a result of this effect the reset phase value does not depend on the initial phase. It is defined only by the stimulus parameters. The autoreset effect can be used for phase synchronization and phase cluster formation in ensembles of autooscillatory units.

The work is devoted to investigation of dynamics of running waves in the ring of Van-der-Pol oscillators with diffusive coupling. Regions of existence and stability are built in the parameters space. Typicalness of appearance of regimes with different wavelengths and regularities of their disappearance are considered. Influence of anharmonicity on multistability of spatio-periodic regimes is studied.

The cluster formation in the cyclic (4+1)-Lattice – Lotka–Volterra model is studied by Kinetic Monte Carlo simulations on a square lattice support. The features of cluster size distribution, spatial autocorrelation function and other dependences of the spatial dynamics of the system are under consideration. The role of cluster formation process and it effect on the systems dynamics is studied in this work. We show that the external mixing added to the initial scheme leads to the periodic self-oscillations appearance.

Numerical calculations of structures, Infrared and Raman vibrational spectra of small water clusters are performed by solution of the molecular SchrÄ odinger equation in the X 3LYP/aug-cc-pVQZ theory. Spectral features and evolution of hydrogen bond properties in clusters with their size growth are discussed. Obtained results may be used in molecular dynamics simulations of water.

We study localization of thermo-convective flows in a shallow horizontal layer subject to a fixed thermal flux across the layer, and the effect of advection on the localization properties. The thermal flux applied is stationary in time and randomly inhomogeneous in space (the problem considered is 2-D; the mean flux is nearly critical). The interpretation of linear results is underpinned by numerical simulation of the original nonlinear problem.

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.

A method is proposed for reconstructing time-delay systems in periodic regime of oscillations. The method is based on the analysis of these systems response to a weak periodic pulse driving. It is shown that proposed method with using of weak driving allows one to recover the delay time of a ring self-oscillating system with time-delayed feedback and to define the order of a model delay-differential equation.

The influence of additive homogeneous isotropic field of Gauss fluctuations of dynamical variables of Gierer–Meinhardt model to formation of dissipative structures in soft mode regime was investigated. The system of equations for description of undamped modes interaction was received. It was shown that fluctuations of dynamical variables are widening the instability region. The numerical simulation of considered model with different boundary condition was performed.

The influence of multiplicative fluctuations of parameters of reaction­diffusion system on example of Gierer–Meinhardt model to formation of dissipative structures in soft mode instability regime was investigated. The system described interaction of non­decreased modes (order parameters) was received. It was shown that fluctuations of parameters are lead to changing of number of unstable modes, shifting of their eigenvalues and parametrical excitation of the system. The numerical simulation of described model evolution was received.

The paper presents the experimental results of the temperature influence on the course of self­oscillating flow Briggs–Rauscher reaction. Account changes in the period of the intensity, speed and time of chemical oscillations. It is shown the changes of the electrode potential during heating and cooling of the reaction solution (oscillation component of the reaction)