Mathematical Approaches in Studying the Ideal Image of the Goal

Abstract

The article outlines the possible approaches in the mathematical computations of integrated behavioral units in functional systems supporting homeostasis through in behavioral changes. By an imbalance in the homeostasis system which initiates adaptive behavior we assume: for metabolism – a departure of the parameters from the “normal zone” to the level of a suprathreshold sensitivity of the receptors; for structures of the psychological and social spectra – to the “cognized-not cognized”, “acceptable-not acceptable” levels. For the system analysis of goal-directed behavior dynamics, we present a combination of the “creation – retention” of the ideal image of the goal and the entire effector structure of the integrated behavioral unit by introducing an integrating term, motivational gradient. The integrated Behavioral Unit (BU) is described as a psychophysiological metamer in behavioral continuum, including a mathematical description of the BU as a whole including its elements viz., the ideal image of the goal and the motivational gradient. The hemodynamic equivalent of the motivational gradient (the scalar gradient) and subjective time (the time marker) are used as the BU markers. For the mathematical description, we use the mathematical apparatus of topological spaces and elements of the string theory to open up opportunities for new approaches in psychology and neurobiology.

Keywords

• integrated behavioral unit;
• ideal image of the goal;
• motivational gradient;
• translation symmetry;
• scalar vector;
• topological space;
• artificial intelligence.