ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Nonlinear Dynamics in Action

Does god dice?

Authors used the simple mathematical models as a base for the discussion of the evolution of  human society.

On the question of two self-exciting oscillation models in non-physical systems

In this article Wilson-Cowan model for interactions of excitatory and inhibitory neurons and model of currency oscillations on a Forex market were considered.

Experimental determination of continuous vibrations in electroconductivity of natural waters

In the process of hydrochemical analysis of natural waters by the direct contact conductometry method the phenomenon of continuous vibrations in specific electroconductivity was discovered for the first time. The possible reasons of the appearance of the vibration process are discussed. 

Rhythmic processes of renal blood flow autoregulation and their interaction in the form of modulation of oscillations

Renal blood flow autoregulation at the level of individual nephrons includes two interacting mechanisms that produce oscillations with different time scales: the tubologlomerular feedback (TGF) and the myogenic response. Based on the wavelet-analysis of experimental data, we study in this work phenomena of amplitude and frequency modulation of myogenic oscillations by the TGF-rhythm. Features of nonlinear dependencies of amplitude and frequency deviation of modulated process versus the amplitude of modulating oscillations are revealed.

Dynamic modes of two­-age population model

In this paper we research a mathematical model of dynamics for the population number. We considered the population of the two-age classes by the beginning of the next season: the younger, one including not reproductive individuals, and the senior class, consisting of the individuals participating in reproduction. The model parameters (birth rate and survival rates) represent the exponential functions of the both age groups numbers. According to this supposition the density-dependent factors restrict the development of population.

Nonlinear models of blood supply dynamics in tissue area

A continual model of tissue blood supply has been suggested in this paper providing the existence of autostructures in the inhomogeneous blood distribution. Theoretical analysis including both analytical and numerical calculations has been carried out on the base of this model. The filtration variations of blood flow caused by medium activity (chemical reactions, nerve excitation) have been studied as well as self-organization processes accounting mechanisms of microvessel regulation.

Does god dice?

Authors used the simple mathematical models as a base for the discussion of the evolution of human society.

Computer modeling of self-organization processes in irradiated solids

Spatial self-organization structures in the metallic materials after irradiation by laser are studied. General method of the computer analysis of such structures using multifractals approaches is described. Founded consistent patterns of the changes of multifractals sets in irradiated surface of solids are used for the modeling of the system at the surface of two-dimensional lattice. 

Bifurcations in nonlinear dynamic models of a gas pool and an underground gas storage facility

The development of a gas pool and operation of an underground gas storage facility are studied as dynamic systems with use of concepts and terms of nonlinear dynamics. For the first time bifurcation diagrams have been constructed for nonlinear dynamic models of a gas pool and an underground gas storage facility. Stability conditions of the processes of the gas pool development and of the underground gas storage facility functioning have been studied.