Petukhov Alexandr Y, Morozov Nikita S, Krasnitskiy Nikolay V, Petukhov Yury V
Information Security Center, Neimark University, 603138 Nizhny Novgorod, Russia.
Microelectronics Center, Neimark University, 603138 Nizhny Novgorod, Russia.
Entropy (Basel). 2025 Mar 10;27(3):287. doi: 10.3390/e27030287.
The objective of this study is to develop a mathematical model capable of correctly displaying the dynamics of an individual's cognitive activity under conditions of external information influence of different modalities. The adequacy of the model is verified by comparing the results of numerical analysis and experimental data. The mathematical basis of such a model is the apparatus of self-oscillating quantum mechanics. To describe algorithms for the processes of transmission, processing, and generation of information, the theory of information images/representations is used. Methods. This article provides a brief description of the proposed theory. The cognitive activity of an individual is represented mathematically as a one-dimensional potential hole with finite walls of different sizes. The internal potential barrier in this model can model the boundary between consciousness and subconsciousness. The authors developed a parameterization of the systems under study taking into account the proposed theory. Next, a mathematical model was developed based on the apparatus of self-oscillatory quantum mechanics. The authors formulated an equation that describes the function of the state of an information image in the process of human cognitive activity. Computer modeling of various variations of information impact was carried out. The authors also conducted a specially designed experiment. Conclusions. The authors have identified characteristic patterns of such processes and shown the oscillating nature of changes in the state function of information images and the appearance of characteristic threshold effects. A comparison of the obtained model and experimental data showed the adequacy of the developed tool (the coincidence of the general dynamics and characteristic patterns was shown).
本研究的目的是开发一种数学模型，该模型能够在不同模态的外部信息影响条件下正确展示个体认知活动的动态变化。通过比较数值分析结果和实验数据来验证该模型的充分性。这种模型的数学基础是自振荡量子力学的工具。为了描述信息传输、处理和生成过程的算法，使用了信息图像/表征理论。方法。本文简要描述了所提出的理论。个体的认知活动在数学上表示为具有不同大小有限壁的一维势阱。该模型中的内部势垒可以模拟意识和潜意识之间的边界。作者考虑所提出的理论对研究的系统进行了参数化。接下来，基于自振荡量子力学的工具开发了一个数学模型。作者制定了一个方程，该方程描述了人类认知活动过程中信息图像状态的函数。对信息影响的各种变化进行了计算机建模。作者还进行了专门设计的实验。结论。作者确定了此类过程的特征模式，并展示了信息图像状态函数变化的振荡性质以及特征阈值效应的出现。对所得模型与实验数据的比较表明所开发工具的充分性（展示了总体动态和特征模式的一致性）。
