Modeling of human cognitive activity under external information influence based on the mathematical apparatus of quantum mechanics

The present article explores the modeling of human cognitive activity in response to external informational stimuli of varying modalities. The mathematical foundation of the proposed model is based on elements of the mathematical apparatus of quantum mechanics, the theory of information images/representations, as well as a new approach to the description of information objects using. The theory of informational images/representations is employed to describe the mechanisms of information transmission, processing, and generation. A brief overview of this theoretical framework is provided in the article. The cognitive activity under investigation is modeled using a one-dimensional potential well with walls of differing heights. Within this interpretation, the internal barrier symbolizes the boundary between the conscious and subconscious levels of the mind. The proposed theoretical approach was then utilized to parametrize the studied cognitive systems. A mathematical model was subsequently formulated, using the principles of self-oscillatory quantum mechanics, leading to the formulation of an equation that describes the state function of an informational image during cognitive processes. In order to investigate various scenarios of informational influence, computer-based simulations were conducted. Consequently, characteristic patterns were identified, including the oscillatory nature of changes in the state function of informational images and the emergence of distinct threshold effects. These findings are in agreement with existing experimental data.