Nonlinear Dynamics in Action

Topic.The article reflects important milestones in the history of the physics and mathematics faculty of Saratov University (1917–1945), which played the role of the most important educational and scientific center of the Volga region and the East of Russia. The faculty was established by the Decree of the Provisional Government on July 1 (14), 2017, and began its work from September of the same year.

The issue of modeling various kinds of social conflicts using diffusion equations is discussed. The main approaches to and methods of mathematical modeling in contemporary humanitarian sciences. The main concepts of social conflicts, ways of their classification, interpretation, including ethnic-social, religious and other conflicts are considered. The notion of a conflict in a social system is defined in terms of mathematical modeling.

On the basis of a simple mathematical model «producers-products-managers», reason, substance, and possible ways of overcoming of a centuries-old conflict in humanity life are considered.

Complication of fractal structure of ammonite’s shells has been considered during ontogeny and phylogeny. Analogy to Koh curves has been presumed. Fractality among ammonites may be considered as adaptive and evolutionary advantage that explains their high rate of evolution and certain causes of extinctions.

We propose a dynamic system determined by a many-dimensional logistic map as a variant of a nonlinear model for dynamics of a biological many-group population. In some parts of a compact phase space the map displays a behavior which is atypical for a one-parameter one-dimensional logistic map. For a many-group population model it means stepwise changes of a total population density and densities of population age groups. We have an opportunity of getting a total population age groups changing periodically with the same period in many various parts of a phase space.

It has been shown in this work how the evolutionary change of alleles’ frequencies, which is accompanied by the growth of average population fitness, leads to chaotic and cyclic dynamics of population size. Then the possible mechanisms of appearance of complicate temporal organization of genetic biodiversity have been considered.

Fractal analysis of natural self-similar structures has been considered. Different approaches to the analysis of abstract mathematical fractals and natural fractals have been described. Numerical method of the fractal dimension calculation has been suggested. This method has been applied both for the model fractal (Sierpi´ nski carpet) and natural fractals (Saratov ravine network).

The analysis of regime parameters daily fluctuations of epuration columns is carried out, and it is proved, that observable noise-like fluctuations in the system dephlegmer – condenser have not stochastic, but the determined nature, and are caused by chaotic character of process dynamics. The system of the ether-aldehyde fractions expenditure stabilization is developed in the structure of automatic control system of ethyl spirit rectification.

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.

The necessity of the considering the historical-geological and paleogeomorphological regularities of the river basin formation in the modeling of natural (river genesis) oil reservoirs structure has been discussed. River network developed at the different geological epochs can not represent the modern river network similarity. Therefore, formodeling the oil reservoirs structure it is necessary to take into account the possible structure differences between old and modern river networks.