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


Nonlinear Dynamics in Action

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.

Does god dice?

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

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 speci?c electroconductivity was discovered for the ?rst 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 wavelet­analysis of experimental data, we study in this work phenomena of amplitude and frequency modulation of myogenic oscillations by the TGF­rhythm. Features of nonlinear depen­dencies of amplitude and frequency deviation of modulated process versus the amplitude of modulating oscillations are revealed.

Dynamic modes of two­age population model

In this paper we research a mathematical model of dynamics for the population number. We considered the population of the two­age 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 density­dependent factors restrict the development of population. Analytical and numerical analysis of the model is made.

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 self­organization 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.

A neural network as a predictor of the discrete map

The possibility of predicting the regular and chaotic dynamics of a discrete map by using artificial neural network is studied. The method of error back­propagation is used for calculation the coefficients of the multilayer network. The predicting properties of the neural network are explored in a wide region of the system parameter for both regular and chaotic behaviors. The dependance of the prediction accuracy from the degree of chaos and from the number of layers of the network is studied.

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.

Study of the earth’s pole motion using a mapping on an external force period

It is known from astronomic observations that the motions of the North pole of the Earth consist of a trend to the Greenland direction, and a rotational component superimposed on the trend. The periods of 12 and about 14 months these motions. The first period is resulted from the seasonal mass redistribution in atmosphere and oceans. The second period is its called the Chandlerian and nature is vague. Because of incommensurability of both periods each with another one can see six/sevel year beats in the time series of the Earth’s pole coordinates.

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