Mathematical Modelling of Delayed Behavior

Author: Nino Archvadze
Co-authors: Sulkhan Tsagareli, Otar TavdiSvili, Marika Gvajaia
Keywords: Delayed behavior; Learning, Algorithm; Markov chain
Annotation:

The aim of the research was the study and modelling of complex perception process in rats by assessing of food-obtaining behavior in T-maze in conditions of two feeding racks. For this purpose mathematical methods were integrated in behavioral study. For the assessment of optimal behavioral strategy across learning process, algorithmic description approach was proposed. The compliance of Markov Chain method for spatial memory behavioral patterns was tested. The modified direct delayed reaction method was used for the evaluation of behavioral conformities across food-obtain spatial learning tasks. Food was provided according to the time-spatial program, in conditions of fixed delay for each feeding rack and inter-trial interval throughout the whole experiment. Chaotic and optimal behavioral algorithms described by consequences “0” and “1” were obtained. The optimal behavioral algorithms for each experimental day have been defined. The mathematical apparatus describing the direct delayed reactions using the discrete - time Markov chains was considered. The behavioral experiment using a modified method of direct delayed reactions made it possible to observe the learning process along with establishing the maximal delay and identifying an optimal algorithm for minimal errors and maximal rewards. From the consequence of the all of theoretically calculated (25 = 32) algorithms chaotic and optimal behavioral algorithms were defined and dynamic of experimentally obtained behavioral algorithms were assessed. Using Markov Chains method transition probabilities were generated which are probabilities of moving from one state to the next. For the modeling of food-obtaining spatial memory tasks the recurrence equation has been proposed. Such approach gave possibility for prognoses of rats’ delayed reactions during spatial memory acquisition tasks. The proposed method was tested for randomly chosen nth trials of 10-trial behavioral tasks. The calculated probabilities for all measured patterns of food-obtaining behavior coincided with empirical probabilities. The compliance of Markov Chains method for prognoses of spatial memory behavioral patterns was demonstrated. Proposed approach made ground for further studies across different behavioral tasks.

Lecture files:

Mathematical Modelling of Delayed Behavior [en]
დაყოვნებული ქცევების მათემატიკური მოდელირება [ka]