# Nonlinear Dynamics in Action

## Some aspects of reconstruction and nonlinear modeling of erosive network in geological past

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 di?erent 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 di?erences between old and modern river networks.

## 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.

## 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 ?rst 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.

## Oscillation processes in the gas pool development and in operation of underground gas storage facility

The gas pool and underground gas storage facility are simulated as nonlinear dynamic systems. For the ?rst time the basic physic and mathematical models of gas density oscillations during the development of a gas pool and operation of an underground gas storage facility have been worked out. It is shown that the occurrence of oscillations is connected with heterogeneity of the reservoir, gas cross-?ows between heterogeneity elements, and ?niteness of velocity of gas pressure disturbances propagation in the reservoir bed.

## Application of nonlinear dynamics methods in the automatized control system of spirit rectification process

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. The revealed features of management object dynamics is took into account.

## The dynamic behavior of genetic structure and population size in the evolution models of limited population

It has been shown in this work how the evolutionary change of alleles’ frequencies, which is accompanied by the growth of average population ?tness, 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.

## Definition of the fractal dimension of saratov ravine network

Fractal analysis of natural self-similar structures has been considered. Di?erent 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).

## Crisis of evolution and a collective people game

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

## Fractal in structure and evolution of cephalopodian mollusca

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.

## Representation of many-group population model as one-species population model with many parameters

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.