<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This article first introduces neural networks and their characteristics. Based on a comparison of the structure and function of biological neurons and artificial neurons, it focuses on the structure, classification, activation rules, and learning rules of neural network models. Based on the existing literature, this article adds a distributed time lag term of the neural network system. In the actual problem, history has a very important influence on the current change situation, and it is not only at a specific time in the past. It has an impact on the current state change rate. Therefore, based on the existing literature that only has discrete time lags, this paper adds distributed time lags. Such neural network systems can better reflect real-world problems. In this paper, we use three different inequality scaling methods to study the existence, uniqueness, and global asymptotic stability of a class of neural network systems with mixed delays and uncertain parameters. First, using the principle of homeomorphism, a new upper-norm norm is introduced for the correlation matrix of the neural network, and enough conditions for the existence of unique equilibrium points in several neural network systems are given. Under these conditions, the appropriate Lyapunov is used. Krasovskii functional, we prove that the equilibrium point of the neural network system is globally robust and stable. Numerical experiments show that the stability conditions of the neural network system we obtained are feasible, and the conservativeness of the stability conditions of the neural network system is reduced. Finally, some applications and problems of neural network models in psychology are briefly discussed.</p>
</abstract>

This article first introduces neural networks and their characteristics. Based on a comparison of the structure and function of biological neurons and artificial neurons, it focuses on the structure, classification, activation rules, and learning rules of neural network models. Based on the existing literature, this article adds a distributed time lag term of the neural network system. In the actual problem, history has a very important influence on the current change situation, and it is not only at a specific time in the past. It has an impact on the current state change rate. Therefore, based on the existing literature that only has discrete time lags, this paper adds distributed time lags. Such neural network systems can better reflect real-world problems. In this paper, we use three different inequality scaling methods to study the existence, uniqueness, and global asymptotic stability of a class of neural network systems with mixed delays and uncertain parameters. First, using the principle of homeomorphism, a new upper-norm norm is introduced for the correlation matrix of the neural network, and enough conditions for the existence of unique equilibrium points in several neural network systems are given. Under these conditions, the appropriate Lyapunov is used. Krasovskii functional, we prove that the equilibrium point of the neural network system is globally robust and stable. Numerical experiments show that the stability conditions of the neural network system we obtained are feasible, and the conservativeness of the stability conditions of the neural network system is reduced. Finally, some applications and problems of neural network models in psychology are briefly discussed.

Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method

Sichuan College of Traditional Chinese Medicine

Department of Accounting and Finace, Faculty of Administrative Sciences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

This article first introduces neural networks and their characteristics. Based on a comparison of the structure and function of biological neurons and...

Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method

Publié en ligne: 27 juil. 2021

Pages: 343 - 352

Reçu: 12 avr. 2021

Accepté: 07 juil. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00029

Mots clés
Inequality scaling method, Differential equation, Artificial neural network, Delay differential equation, Psychology

© 2021 Hong Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method

Publié en ligne: 27 juil. 2021

Pages: 343 - 352

Reçu: 12 avr. 2021

Accepté: 07 juil. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00029

Mots clésInequality scaling method, Differential equation, Artificial neural network, Delay differential equation, Psychology

© 2021 Hong Zhang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Mots clés
Inequality scaling method, Differential equation, Artificial neural network, Delay differential equation, Psychology