Autowaves. Self-organization

Dynamic chaos – a remarkable milestone development of science of the last centuryhas attracted the attention of different areas of knowledge. Chaos theory describes not only a wide range of phenomena in various fields of physics and other natural sciences and penetrates into the humanitarian sphere, but also significantly influenced the scientific picture of the world. What features of the development of science, economic and social conditions led to that long and difficult path of discovery of chaos began precisely at the end of the XIX century and stretched out for decades?

We explore phase multistability which takes place in an ensemble of periodic oscillators under the action of long-distance couplings, which appear randomly between the arbitrary cells. The  system under study is Kuromoto’s model with additional dynamical interconnections between phase oscillators. The sequence of bifurcations, which accompany increasing of the strength of the global coupling is determined. Regions of multistability existance are defined.

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.

This paper presents two new methods of suppressing an impulse in one-dimensional and two-dimensional excitable media using an external influence. In the proposed methods, we used short-impulseinfluence, leading to a change in velocity of the front , which in turn led to the destabilization of  the propagating impulse and transition medium unexcited state. The studies were conducted on the Zykov model that a certain set of parameters is a model of an excitable medium.

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.

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.

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.

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

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 work presents the results of experimental investigation of roller domains parametrically excited by the capillary waves. Domains rollers were oriented parallel to the different 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 different 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.