具分布时滞的单向神经网络模型的分支分析.docVIP

具分布时滞的单向神经网络模型的分支分析 韩艳艳，宋永利 同济大学数学系，上海200092 摘要：在这篇文章中，我们研究了分布时滞对三元环形神经网络系统的动力学的影响。以平均 时滞为参数，我们得到了两个Hopf分支的临界值。用多尺度方法，分支方向和周期解的稳定性 被完全确定。 关键词：神经网络；分布时滞；Hopf分支；分支方向；稳定性 中图分类号： O175 Bifurcation analysis in a unidirectional ring of neural networks with distributed delays HAN Yan-Yan, SONG Yong-Li Department of Mathematics, Tongji University, Shanghai 200092 Abstract: In this paper, we consider the e?ect of distributed delays on the dynamics in a three-neuron unidirectional ring. Taking the average delay as a bifurcation parameter, we ?nd two critical values at which the system undergoes Hopf bifurcations. The direction and t The orbital asymptotic stability of the Hopf bifurcating is determined by using the method of multiple scales. Key words: Neural network; Distributed delay; Hopf bifurcation; Direction of bifurcation; Stability 0  Introduction An arti?cial neural network (often just called a ‘neural network’ (NN)) is an information processing paradigm that is originally inspired by the biological nervous systems such as the brain. Arti?cial neural networks are composed of interconnecting arti?cial neurons or nodes and may either be used to gain an understanding of biological neural networks, or for solving arti?cial intelligence problems without necessarily creating a model of a real biological system. It has been shown that neural network models possess good potential applications in di?erent areas such as associative memory, pattern recognition, signal and image processing and opti- mization (see [1? , 2], and the references therein). One of the classical and best understood 基金项目： Supported by Doctoral Fund of Ministry of Education of China (No.200802471024) 作者简介： Han Yan-Yan (1987-)，female，graduate student, major research direction：theory of functional di?erential equations and applications. Corresponding author: Song Yong-Li (1971-)，male，associate professor， major research direction：theory of functional di?erential equations and applications. examples of