When you comprehend it implement it

It is not your enemy

who takes money and power,

but who makes your lifetime aimless.

Introduction

The problem of qualitative description of solution of equations that model a certain dynamical system is directly related with definition of ranges of admitted and critical values. The fundamentals of the modern approach to study of qualitative changes in behavior of solutions of ordinary differential equations were created by A. Poin­care more than 100 years ago. He was the first to introduce such notions as structural stability, dynamical stability and critical sets. A. Poin­care paid special attention to study of qualitative changes of a system in the course of change of its functional properties. A. Lyapunov followed this direction in study of critical solutions of equations, when he was creating the theory of bifurcation. Afterwards, only in the 1930^th, Soviet mathematicians A. Andronov, L. Pontryagin again referred to Poincare’s ideas in the course of developing of the concept of structural stability.

Today, there is need in theories related to investigation of such dynamical systems as the biosphere [18], the sociosphere and the egosphere. Are all problems of the space and the geosphere can be considered exhausted? All depends on the goal under investigation. If consider the role and the significance of losses caused by systems that exist in human life, then this sphere of human activity is important today.

There were several stages for human in the course of development of theoretical fundamentals of synthesis and analysis of a dynamical system:

The 1^st stage took place yesterday, when only mechanical (physical) systems were considered;

The 2^nd stage takes place today, when dynamical systems are considered in the presence of human;

The 3^rd stage is when a dynamical system is considered at the structural-functional level with regard to structural-functional properties of human.

The theory of risk concerns the development of calculation methods of dangerous conditions that are specific to operating dynamical systems influenced by external and internal disturbing risk factors.

The theory of risk includes:

— the theory of construction of ranges of safe and dangerous conditions of dynamical systems;

— the theory of probabilistic analysis of dangerous and safe conditions of dynamical systems.

The safe condition of a dynamical system can be provided when:

— the range of its admitted (safe) conditions is known;

— proximity to the border of the admitted conditions range is detected by means of a controlling system;

— the system possesses the managing means that prevent it from leaving the admitted conditions range.

Any dynamical system provides its operation by including into its structure the following:

— the efficiency management system;

— the risks management system.

The qualitative theory of dynamical systems in the risk field includes some parts of the dynamical system qualitative theory at the structural level.

There are two levels of fundamental organization: structural and functional as well as two levels or approaches to description of laws – macroscopic and microscopic. The first approach is related to reversible dynamical laws, the second one – to irreversibility expressed by statistic laws. Today, we explore the world, build models from material things to spiritual ones, from elementary things to complex ones, from the condition to the structure of a system or an object which implements this condition. I.e. by perceiving the fundamentals, we want to perceive the structural-functional basis of the whole of the objective reality or its separate objects and systems. And the unity of the following two ways is necessary: “from the general to the special” and “from the special to the general” – we’ll find the truth in some point between them.

Biosphere biosystems, biosocial environment social systems are open systems that are statistically non-equilibrium. These systems are managed by the laws that specify nonlinear processes both at the output of a dynamical system and within it. Nonlinearities specified with structural-functional dynamics provide the capability of self-organ­ization – including due to the capability of resonance response to external influences. Nonlinear effects disable the predictability of the con­dition of a dynamical system towards both directions (“+” and “–”) – before and after, correspondingly.

In order to form the management of risks of dynamical systems at the hierarchical level, structural-functional modeling is developed.

Structural-functional unity of objects and systems of the objective reality is considered in case when functional purposes of subsystems of the structure are common and include: definition of objectives, acquisition of objectives, implementation of objectives, estimation or control of objectives implementation.

Theoretical fundamentals of structural-fundamental modeling of systems consist of two levels:

— qualitative: structural-functional synthesis implemented by all humanists – from theoreticians to practicians;

— quantitative: structural-functional analysis implemented by all naturalists – from application experts (practicians) to theoretician-mathematicians.

In the monograph, the basic attention is given to dynamical systems created in the course of human living activity, and first of all – to the social-economical system as well as to the systems related with human living activity (the biosphere, the ethnosphere, the theosphere).

The dynamical systems class also includes human (the egosphere). The latter demonstrates the evolution of structural-functional properties of all of its four subsystems.

At each stage, the egosphere was a self-organizing system. Though it contained all subsystems, their functional properties radically differed from the today’s ones. They were different in levels of the processes performed by subsystems of objectives definition, acquisition, implementation and control. At the first level, human was satisfied with gifts of nature. At the second level, he learned to make fire, began obtaining food for future use killing the living matter. In the course of self-protection of human, the soul (hippocampus) matured, and its development was specified by natural conditions. It is the level of Homo.

A the third level, spirit or the noosphere matures, teachings of Divine wisdom appear, human forms the objective and the meaning of life worshiping God. Homo sapiens matured here.

The last stage of development formed recently, when the noosphere theory allied with the practical experience created with body labor i.e. when analytical mind was involved into action. Finally, today’s level is Homo sapiens faber.

Each stage is specific for its own levels of energy-intellectual potential. And human possesses the structure and develops subsystems (the ones he needs), energetically fills them with information in the form of processes that provide acquisition of the objective and the meaning of life.

Evolution of dynamical systems performed in the course of human living activity can be observed in social-economical systems. For example, the international economical system, a structure consisting of subsystems with the corresponding functional properties, is a dynamical system. Structural-functional properties of this system evolve on the basis of international division of labor: intellectual, technological and technical. Globalization of the international economy takes place basing on structural-functional implementation principle with unification of structural division resources and intellectual capabilities.

Finally, today there are international banking and market systems that manage the pricing at the following markets: financial, labor, commodities and services, natural resources.

The book comprises the results of creation of fundamentals of synthesis and analysis of structures that form the basis of dynamical systems that were created and are being created today, the basis of their interrelation and difference that provide their safe conditions in the course of their operation.

The necessary condition of safe operation is provided by means of structural-functional synthesis of a risks and safety management system. The sufficient condition of safety is provided by means of structural-functional analysis.

In spite of the great amount of works performed by the Author that were referred to in this book, I consider that the book comprises the derivation of the problem under the general name “Risks and safety of human activity”. The honor to perceive and develop the essential properties of this problem is given to the other theoreticians.

I would like to express myself, my spirit, spiritual life in order for a man to read, think and continue his living activity. Another one wants to express his own ideas in the form of fundamental work: with the aim for a man to read, understand everything and be guided by the read, for there is nothing to continue – everything is done!

The book was written for those who are interested in problems of human activity risks.

E.B. Savva made a great contribution to the present work at the stage of its implementation in the form of monograph.