测度神经网络的同步问题
Measure Neural Network Synchronization
DOI: 10.12677/AAM.2025.1412522, PDF,   
作者: 金 凡：浙江师范大学数学科学学院，浙江 金华
关键词: 同步；李雅普诺夫定理；测度；Synchronization； Lyapunov Theorem； Measure
摘要: 本文提出了一种创新框架，用于分析神经网络中的同步问题。该框架采用测度微分方程 (MDEs)， 能有效刻画实际系统固有的不连续特性和动态行为。由于测度函数的引入，以及系统不连续点的 存在，传统的同步分析方法需重新审视，并配以专门的计算手段。本研究的核心贡献在于，在测 度微分方程框架下建立了新的李雅普诺夫定理，据此为系统构造了与之相适应的李雅普诺夫函数。 这项工作不仅深化了对神经网络同步机理的理论认识，也彰显了测度理论在复杂网络分析中的重 要性。
Abstract: This paper proposes an innovative framework for analyzing synchronization in neu-ral networks by employing measure differential equations (MDEs), which effectively capture discontinuities and dynamic behaviors inherent in real-world systems. The incorporation of measure functions necessitates a re-evaluation of traditional synchro- nization analysis, as the presence of discontinuity points demands specialized compu- tational approaches. A key contribution of this work is the development of a new Lyapunov theorem within the MDE framework, which facilitates the construction of a tailored Lyapunov function for the system. This study advances the theoretical un- derstanding of synchronization in neural networks and underscores the significance of integrating measure theory into the analysis of complex networks.
文章引用：金凡. 测度神经网络的同步问题[J]. 应用数学进展, 2025, 14(12): 468-483. https://doi.org/10.12677/AAM.2025.1412522

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