Cybernetical actions—Constraints and orderliness in biological populations

The concept of a cybernetical action is defined as an action leading to a certain goal, subject to some constraints, by choosing the most appropriate (optimal) way. It is shown that cybernetical actions play a fundamental role not only in organisms (synaptic events, O₂ transport system hierarchy, etc.), but also in biological populations (neuron populations, bacterial populations, social populations of insects, etc.). They lead to new orderly structures (states) in the population under consideration, according to the pursued goal, by using informations conveyed by the so calledactive messages defined in a previous paper (Teodorescu, 1976c). When stored (or generated) in a subsystem these active messages lead tocybernetical models, implicated in the muscle control phenomena, as well as in the optimal adaptive models of motion. Thus, mathematical models of the active messages are defined, namely themessage operators and an axiomatic theory is developed, emphasizing their main properties. They may be regarded as operators in a wider sense, involving an optimization. Moreover, message operators are comparable by using the concept ofstrength. Thus, the concepts ofcodex andmetacodex (as fundamental sets of message operators) are defined. It is shown that message operators involved by the codex (Ω) are always able to perform transitions from a given orderly state (F ₀), to a new orderly state (F), whereF's are elements of a particular metric space, ℱ, satisfying someconditional metric properties. (“Distances” are conditioned by the states of the initial random process.) This fact emphasizes the central role played by the intrinsic features, i.e. “aptitudes”, of the biological population, in performing a cybernetical action. Hence, a cybernetical action may be defined as a tripletA =(Ω, ℱ, S) involving the codex Ω, the space ℱ as well as the domainS of the possible states of the initial random process (real numbers associated to the possible outcomes). A mathematical model of the cybernetical action is, thus, obtained which leads to a deeper understanding of the transformations performed by active messages in biological populations, as well as to new investigation tools in biology.

Authors and Affiliations

1. Trandafirilor 2, Timisoara, Romania

   D. Teodorescu

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