Effects Of Delays On The Basin Boundary Of Attraction In A Hopfield Network Of Two Delay-connecting Neurons

Jian Xu; Hui-lin Shang; Yu Huang

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Effects Of Delays On The Basin Boundary Of Attraction In A Hopfield Network Of Two Delay-connecting Neurons

机译：时延对两个时延连接神经元Hopfield网络中吸引域边界的影响

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A continuous-time Hopfield neural network with two delay-connecting neurons is considered in this paper. Some sufficient conditions for the number and delay-independent stability of the equilibria in the network are given analytically. It is necessary to classify the attraction domains since multiple attractors coexist when the sufficient conditions are satisfied. Thus, effects of the delays on the boundary separating the basins of attraction of the stable equilibria are investigated analytically and numerically. The results show that the evolution of the boundary depends on the delays and is neither simple nor intuitive even if the delays do not affect the stability of attractors. The results provide also the possibility to design the network according to the memory pattern and storage.

机译：本文考虑了具有两个延迟连接神经元的连续时间Hopfield神经网络。通过分析给出了网络中均衡数量和独立于延迟的稳定性的一些充分条件。由于满足足够条件时多个吸引子共存，因此有必要对吸引域进行分类。因此，分析和数值研究了延迟对分离稳定均衡吸引盆的边界的影响。结果表明，边界的演化取决于延迟，即使延迟不影响吸引子的稳定性，边界的演化也不简单也不直观。结果还提供了根据存储模式和存储设计网络的可能性。

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来源
《Nonlinear dynamics, psychology and life sciences》 |2009年第2期|161-180|共20页
作者
Jian Xu; Hui-lin Shang; Yu Huang;
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作者单位

Tongji University, Shanghai, P. R. China;

Tongji University, Shanghai, P. R. China;

Tongji University, Shanghai, P. R. China;

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原文格式 PDF
正文语种 eng
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关键词
delay differential equation; neural network; basin of attraction; stability; self-feedback control;

机译：时滞微分方程;神经网络;吸引力域;稳定性;自反馈控制;

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1. Effect of Delay on the Boundary of the Basin of Attraction in a Self-Excited Single Graded-Response Neuron [J] . Pakdaman K, Malta C, Grotta-Ragazzo C, Neural computation . 1997,第2期

机译：延迟对自激单梯度反应神经元吸引盆边界的影响
2. Multistability and New Attraction Basins of Almost-Periodic Solutions of Delayed Neural Networks [J] . Wang L., Lu W., Chen T. Neural Networks, IEEE Transactions on . 2009,第10期

机译：时滞神经网络的概周期解的多重稳定性和新的吸引域
3. Stability and Hopf-Bifurcating Periodic Solution for Delayed Hopfield Neural Networks with n Neuron [J] . Haji Mohammad Mohammadinejad, Mohammad HadiMoslehi, Erik VanVleck Journal of applied mathematics . 2014,第Pta5期

机译：具有n个神经元的延迟Hopfield神经网络的稳定性和Hopf分岔周期解
4. Spurious Minima and Basins of Attraction in Higher-Order Hopfield Networks [C] . M. Atencia, G. Joya, F. Sandoval 7th International Workshop-Conference on Artificial and Natural Neural Networks, IWANN 2003 Pt.1 Jun 3-6, 2003 Mao, Menorca, Spain . 2003

机译：高阶Hopfield网络中的虚假极小值和吸引域
5. Global attractors of delay differential systems arising from networks of neurons. [D] . Chen, Yuming. 2000

机译：由神经元网络引起的延迟差分系统的全局吸引子。
6. Modeling Basins of Attraction for Breast Cancer Using Hopfield Networks [O] . Alessandra Jordano Conforte, Leon Alves, Flávio Codeço Coelho, 2020

机译：使用Hopfield网络为乳腺癌吸引区建模
7. Modeling Basins of Attraction for Breast Cancer Using Hopfield Networks [O] . Alessandra Jordano Conforte, Leon Alves, Flávio Codeço Coelho, 2020

机译：Hopfield网络建模乳腺癌吸引力盆地

Effects Of Delays On The Basin Boundary Of Attraction In A Hopfield Network Of Two Delay-connecting Neurons

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