Nonlinear Dynamics in Action

We discuss the conception of the adaptive modeling of the natural oil reservoirs. This conception is based on application of simple mathematical algorithms to imitate the physical processes, defining the reservoir structure. As an example the possibility of fluvial reservoir modeling by a cellular automata is considered.

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.

The gas pool and underground gas storage facility are simulated as nonlinear dynamic systems. For the first 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-flows between heterogeneity elements, and finiteness of velocity of gas pressure disturbances propagation in the reservoir bed.

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.

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

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.

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.

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.

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.

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