математическое моделирование

In experimental studies of the propagation of combustion waves in gaseous media, it was found that, under certain conditions, autowave – spiral or target – patterns appear at the wave front. The purpose of the present study is to propose a mathematical model that can explain this phenomenon based on the known chemical kinetics of hydrogen combustion. Model. The original detailed model was first reduced to four equations that adequately describe the propagation of the combustion wave.

The purpose of this work is to show the mechanisms of transitions between different dynamic modes of spontaneous astrocytic calcium activity. With this aim, dynamics of recently introduced Lavrentovich–Hemkin mathematical model was examined by both analytical and numerical techniques. Methods. In order to obtain the conditions for the oscillations cessation, the linear stability analysis for the equilibrium point was carried out. Complicated dynamics was studied numerically by calculations of time traces and bifurcation diagrams. Results.

Goal. The paper is devoted to controlling the dynamics of spike neural networks by local periodic stimulation of various network sections. Methods. The simulation uses a network of synaptically connected spike neurons distributed in two-dimensional space. The dynamics of the transmembrane potential of neurons is described by the Izhikevich model, short-term synaptic plasticity is represented by the model Tsodyksa–Markram, the effects of changes in the efficiency of connections between neurons are modeled using spike-timing-dependent plasticity (STDP). Results.

Purpose. The article is devoted to modeling the socio-political development of Russia in 1910–2009 based on the author’s socio-energy approach. In this paper, we briefly talk about the basics of the proposed approach, its principles and basic equations. Methods. The mathematical model is based on the Langevin diffusion equation. We also introduce the concepts of social energy, coefficients of the state of society and give them definitions. Results.

We propose new mathematical models of the evolution of the human society based on the synergistic approach. They describe the dynamics of the indicators of the major integral development of the World-System such as the total population and the level of the technological development. Our models capture the basic laws of the space and temporal development of the society. They indicate the hyperbolic growth of the population that agrees with the demographical data and the cyclic dynamics.

Built in a cell synthetic gene regulatory elements may function rather independently on the original natural system. Experimental and theoretical studies of small synthetic networks allow for a better understanding of fundamental dynamical mechanisms of gene regulation. This paper gives an introduction to the modern mathematical approaches and methods in this field, primarily in the framework of nonlinear dynamics.

Several mathematical models of volume free electron lasers are described with the aim of investigation of their nonlinear dynamics. This review includes models of beams of charged particles moving through spatially-periodic systems (photonic crystals). In simulation of volume free electron lasers on the base of photonic crystals made from metallic threads or foils working in the microwave range it was shown the necessity of taking into account dispersion of electromagnetic waves on resonator threads.