CYBERNETICAL ACTIONS AND MARKOV PROCESSES

Abstract

A goal-oriented action that is performed by a biocybernctical system, with minimum losses, subject to some constraints, is termed cybernetical action. Actions of this kind (often related to survival, e.g., defense or predatory actions) are widespread in nature. A mathematical model of these actions, based on a special kind of operators, termed message operators (or optimization operators), is investigated in connection with the customary transition matrices used in the theory of Markov processes. It is shown that, under certain conditions, transition matrices may be regarded as a special kind of message operators; hence, most of the properties of Markov chains can be expressed in terms of the latter ones. Accordingly, a new class of “stochastic processes with optimization” is defined, which enables Markovian as well as non-Markovian evolutionary processes to be modeled in a general way. Furthermore, by taking into account some recovery phenomena (related to biological rhythms) a new model of sequential actions is suggested. It is shown that the corresponding stochastic process with optimization always involves adaptive learning (that is, the action is stored in the memory of the system, in its optimal form). Thus, by including in the mathematical model the fundamental “optimization principle” which is inherent to the nature of any biological system, a new tool is obtained, permitting to investigate some unknown aspects of the biocybernctical systems in a more general manner as compared with the customary means.