Fractional Dynamics and Multi-Slide Model of Human Memory

Ihor LubashevskyUniversity of Aizu, Aizu-Wakamatsu, Fukushima, Japan
Bohdan DatskoInstitute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences, Lviv, Ukraine

Abstract

We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of new memory traces caused by learning a certain fragment of information pattern and affected by the fragments of this pattern already retained by the current moment of time. Using the available psychological and physiological data these constructions are justified. The final equation governing the learning and forgetting processes is constructed in the form of the differential equation with Caputo type fractional time derivative. Several characteristic situations of the learning (continuous and discontinuous) and forgetting processes are studied numerically.

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Fractional Dynamics and Multi-Slide Model of Human Memory (435 KB)



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