Subject(s): CX.11, CX.07, CX.18, CX.19, CX.3

Category: Article

Abstract:

The present paper is devoted to one of the fundamental problems of how complex ''living'' systems widely met in nature can adapt to changes in the environment. By the term ''living'' system we mean one that comes into being, provides for itself, and develops pursuing its own goals. This class comprises a great variety of biological, economic and ecological systems. We develop mathematical model of such systems. This model takes into account several fundamental issues of such systems. So it is assumed that systems under consideration to consist of a two subsystems: distributed ''living'' medium and a hierarchical ''supplying'' network. We propose a cooperative mechanism of self-regulation by which the system as a whole can react perfectly. This mechanism is based on an individual response of each element to the corresponding small piece of the information on the state of the ''living'' medium. The conservation of flux through the supplying network gives rise to a certain processing of information and the self-consistent behavior of the elements, leading to the perfect self-regulation. The corresponding equations governing the ''living'' medium state are obtained.We present mathematical models and investigate properties of typical examples of such systems. Economic market and distributed Lottka-Volterra model for ecosystems are considered in detail.

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