# Autowaves. Self-organization

## Two-dimensional self-organized critical sandpile models with anisotropic dynamics of the activity propagation

We numerically and analytically investigate two self-organized critical sandpile models with anisotropic dynamics of the activity propagation – Dhar–Ramaswamy and discrete Feder–Feder models. The full set of critical indices for these models is theoretically determined. We also give systematical statement of the finite-size scaling ansatz and of its use for the solving of self-organized critical systems.

## Spatial-temporal patterns in a multidimensional active medium formed due to polymodal interaction near the wave bifurcation

Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out. It is shown that as a result of competition between modes depending on the value of the parameter defining the strength of interaction only two regimes are possible: either quasi one-dimensional travelling waves (there exists only one nonzero mode) or standing waves (al the modes are nonzero).

## 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.

## Solution of two-dimensional self-organized critical manna model

We propose a full solution for Manna model – two-dimensional conservative sandpile model with the rules of grains redistribution isotropic at the average. Indices of the probability distributions of avalanches main characteristics (size, area, perimeter, duration, topplings multiplicity) are determined for this model both from theory and from simulations. The solution bases on the spatiotemporal decomposition of avalanches described in terms of toppling layers and waves.

## Dynamics of roller domains at parametric excitation of capillary waves in rectangular geometry boundary

The work presents the results of experimental investigation of roller domains parametrically excited by the capillary waves. Domains rollers were oriented parallel to the di?erent borders of the rectangular cell and perpendicular to each other. Found that depending on the initial and boundary conditions on the edges of the cell can emerge two-dimensional domains of di?erent forms. The dynamics of the domain is determined by the movement of their fronts. A model is proposed to explain the observed phenomena, numerical calculations by which agree well with experiment.

## Investigation of particularities formation spatially periodic structures of multieddy isothermal electroconvection

Electroconvective ?ow in plane horizontal layer of dielectric liquid due to the crisis of the equilibrium layer stability loss in homogeneous electric ?eld are numerically modeled.

## Influence of terahertz electromagnetic radiation on the frequency of absorption of molecular oxygen on briggs–rauscher oscillating reaction

In the article the description of the influence of electromagnetic radiation on the frequencies characterizing the maximal absorption intensity and atmospheric oxygen radiation on the process of Briggs–Rauscher reaction has been provided. It has been shown that the radiation increases the time of the oscillation regime more than for 20 % in comparison to an unirradiated flask because of the intensification of the process of oxygen selection.

## External synchronization of traveling waves in an active medium in self-sustained and excitable regime

The model of a one-dimensional active medium, which cell represents FitzHugh–Nagumo oscillator, is studied with periodical boundary conditions. Such medium can be either self-oscillatory or excitable one in dependence of the parameters values. Periodical boundary conditions provide the existence of traveling wave regimes both in excitable anself-oscillatory case without any deterministic or stochastic impacts.

## Stability of a stationary critical state in a model of cluster formation

The paper considers a selforganized critical process of clasterization. The stability of the equilibrium for infinite system of the differential equations approximating this process is proved.

## Spatial-temporal patterns in active medium caused by diffusion instability

The results of investigation of reaction-diffusion type models demonstrating diffusion instability are presented. In particular, in general case the condition for both Turing and wave instabilities are obtained for three equations of this type with the diagonal diffusion matrix. Qualitative properties of the system, in which bifurcations of each of the two types can take place, are clarified. Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out.