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# Graphs of Long-Term Memory as a function of time in the following case: (a) when 0.00, 0.30, ! 0.25 (red) (b) when 0.50, 0.00 , ! 0.25 (blue) (c) when 0.50 , 0.30 , ! 0.00 (black) using bottom-up processing model. Initial values: 0 0, 0 0 Q@R 0 0 .Other parameters remain fixed.

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This research work studies the human brain information processing dynamics by transforming the stage model formulated by Atkinson and Shiffrin into two deterministic mathematical models. This makes it more amenable to mathematical analysis. The two models are bottom-up processing mathematical model and top-down processing mathematical model. The bo...

## Contexts in source publication

**Context 1**

... this chapter, we discuss the results of the numerical experiments carried out. The plots of these results are shown in Figures (4)-(9). ...

## Citations

... An advanced numerical model that can International Journal on Engineering, Science and Technology (IJonEST) 324 represent the biochemical process is greatly needed to better understand and quantify how a unique individual learns. Shikaa and Ajai built upon a logistical model first presented by the AS theory by introducing the Hicklin's concept of dynamic equilibrium theory to represent the concept of mastery learning (Shikaa & Ajai, 2015;Hicklin, 1976). Bush and Mosteller proposed learning as a combination of a myriad of factors related to probability (2006) while Anderson recognized that there was a rate-based element of a potential learning model (1983). ...

Human cognition and consciousness are perhaps the most confounding mystery. Somehow it has a linkage to the process of learning and storage of short-term and long-term memory in the form of knowledge. This paper examines a brief background of early models in learning presented by Atkinson and Shriffrin (1965) and related stochastic models utilizing probability functions. Each of these learning models capture certain facets of the learning process but are ineffective in describing the physical basis in which learning occurs. For this reason, this paper explores analogous mathematical models based on reaction kinetics that have been shown to represent chemical reactions found in nature. Six learning models are presented of unitary, binary, reversible binary, reversible binary with mass action, and enzyme learning model reactions with and without decay. Preliminary analysis of time series plots, phase line diagrams, and phase plane plots were conducted to illustrate equilibrium conditions and stability of the models. Each model is examined in terms of its limitations in the philosophy and inability to capture certain elements that are understood about the learning process. Finally, this paper concludes that the feasibility of understanding behavior such as stability through the tools of applied mathematics and thereby illuminating certain layers of human cognition and learning is a useful tool in examining the suitability of a possible deterministic model that could describe the learning process. Further analysis with empirical data would validate the suitability of the presented models.