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

• Autores: Hong Zhang, Iyad Al Khatib, Hafnida. Hasan
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 7, Nº. 1, 2022, págs. 343-352
• Idioma: inglés
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• Resumen

  • This article first introduces neural networks and their characteristics. Based on a comparison of the structure and functionof biological neurons and artificial neurons, it focuses on the structure, classification, activation rules, and learning rules ofneural network models. Based on the existing literature, this article adds a distributed time lag term of the neural networksystem. In the actual problem, history has a very important influence on the current change situation, and it is not onlyat a specific time in the past. It has an impact on the current state change rate. Therefore, based on the existing literaturethat 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, andglobal asymptotic stability of a class of neural network systems with mixed delays and uncertain parameters. First, usingthe 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. Underthese conditions, the appropriate Lyapunov is used. Krasovskii functional, we prove that the equilibrium point of theneural network system is globally robust and stable. Numerical experiments show that the stability conditions of the neuralnetwork system we obtained are feasible, and the conservativeness of the stability conditions of the neural network systemis reduced. Finally, some applications and problems of neural network models in psychology are briefly discussed.