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Self-organization in essentially nonlinear dynamic systems with probabilistic ordering parameters


Yu. N. Kolomiytsev

The necessity of the examining the processes of self-organization in vomplicated systems, which behaviour is of probabilistic character, is determined by the fact that such systems predominate in the animate nature and society, that is why they are of such a great interest for the science and practice. These examinations are aimed at getting a universal formalized device for operating with the processes of self-organization in order to produce complicated systems with set-up in advance parameters in technique and, perhaps, in the sphere of the social systems. It is obvious that the points of controllability, stability and predictability of the social processes and systems development are not only of merely scientific interest, but they also have a great practical meaning, which is proved by the last events in the world. Two peculiarities of the processes of self-organization are distinguished: 1. Self-organization may be observed only in the systems with large (countless) quantity of the elements and with probabilistic character of the connections between them. The requirement of the self-organization is the “openness” of the system and considerable dynamism of the numerous elements of it and that of the surroundings of this system as well as the ability of the systems to exchange energy and material with the environment simultaneously securing the necessary order level owing to the entropy increase of the environment. 2. The processes of self-organization have practically purposeful but at the same time natural and spontaneous (as everybody reckons) character. The information about the quantity of elements and the connections between them is proved by experimental data but the contradiction between the purposefulness and the spontaneity of the processes of self-organization has not been explained so far. The reference to the order parameters which are immanent to the system is not efficient, because if the defining of the aim lacks, the order parameters are being formed in the process of self-organization at random. Synergy as a scientific theory gives only the description of the processes of self-organization so far and no description of their origin reasons. Avoiding this problem some scientists reckon that the property of self-organization is an attribute of the substance. Such interpretation withdraws the question of self-organization reasons but it simultaneously withdraws the question of controllability, stability and predictability of the processes of self-organization, that is why it does not seem to be constructive. On the other hand the processes and the results of self-organization significantly depend on the properties of the environment, because each system functions in the environment and is a part of it. That is why it will be more productive to affirm that self-organization reasons are to be sought in the process of the interaction of the elements with the environment, which requires broadening the horizon of the research. The article describes the features of self-organization processes in essentially nonlinear dynamic systems with p-robabilistic ordering parameters in the conditions of two-forked energy, substance and information exchange with the environment. The article points out that in case the power of external energy source is limited, the time of existence of dissipative systems is fundamentally restricted, regardless of the opinion that exchange processes are fully reversible in the process of self-organization. The article also reveals some problems and the range of applicability of synergy as of a scientific theory that should be applied equally and together with the other theoretic disciplines.

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