математическое моделирование

The authors propose a complex approach for the analysis of composite materials, including the fundamental models of the nonlinear dynamics, model of effective medium and the theory of electrical circuits. The composite consisting of spherical inclusions in the matrix is considered. The simulation of composite material is carried out by various methods.

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The characters of the article are Nicolas Rashevsky, Karl Ludwig von Bertalanffy and Erwin Schrodinger. The events connected to their scientific research in the sphere of  Mathematical Biology take place up to the end of the World War II. The biggest part of the article focuses attention on Erwin Schrodinger’s book «What Is Life? The Physical Aspect of the Living Cell». This book is known by many, but not many people read it.

It was stated in the paper the mathematical model and its numerical realization for the investigation of wideband chaotic oscillations and of physical processes in the electron beams with virtual cathode at the generators with electron feedback. Also it was briefly described the developed program package for the modeling of non­stationary nonlinear physical processes at the electron generators with virtual cathode and for calculating of output characteristics of devices.

Mathematical model of Volume Free Electron Lasers (VFEL) is described. Some aspects and origins of VFEL chaotic dynamics are examined.

The conceptual model and computer simulations results of path integration in free­scalable nonlinear oscillator neural networks with even cyclic inhibition (ECI­networks) are discussed in this paper. To estimate the phase shifting under input impact the ECI­networks contain two subsystems namely reference and information ones. The population of reference (nonencoding) oscillatory units has significant role in generation and stabilization of numerous time scales despite it don’t assist directly in the phase pattern encoding of input signals.

Several mathematical models of volume free electron lasers are described with the aim of investigation of their nonlinear dynamics. This review includes models of beams of charged particles moving through spatially­periodic systems (photonic crystals). In simulation of volume free electron lasers on the base of photonic crystals made from metallic threads or foils working in the microwave range it was shown the necessity of taking into account dispersion of electromagnetic waves on resonator threads.

We propose new mathematical models of the evolution of the human society based on the synergistic approach. They describe the dynamics of the indicators of the major integral development of the World-System such as the total population and the level of the technological development. Our models capture the basic laws of the space and temporal development of the society. They indicate the hyperbolic growth of the population that agrees with the demographical data and the cyclic dynamics.

Built in a cell synthetic gene regulatory elements may function rather independently on the original natural system. Experimental and theoretical studies of small synthetic networks allow for a better understanding of fundamental dynamical mechanisms of gene regulation. This paper gives an introduction to the modern mathematical approaches and methods in this field, primarily in the framework of nonlinear dynamics.