• 文献检索
  • 文档翻译
  • 深度研究
  • 学术资讯
  • Suppr Zotero 插件Zotero 插件
  • 邀请有礼
  • 套餐&价格
  • 历史记录
应用&插件
Suppr Zotero 插件Zotero 插件浏览器插件Mac 客户端Windows 客户端微信小程序
定价
高级版会员购买积分包购买API积分包
服务
文献检索文档翻译深度研究API 文档MCP 服务
关于我们
关于 Suppr公司介绍联系我们用户协议隐私条款
关注我们

Suppr 超能文献

核心技术专利：CN118964589B侵权必究
粤ICP备2023148730 号-1Suppr @ 2026

文献检索

告别复杂PubMed语法，用中文像聊天一样搜索，搜遍4000万医学文献。AI智能推荐，让科研检索更轻松。

立即免费搜索

文件翻译

保留排版，准确专业，支持PDF/Word/PPT等文件格式，支持 12+语言互译。

免费翻译文档

深度研究

AI帮你快速写综述，25分钟生成高质量综述，智能提取关键信息，辅助科研写作。

立即免费体验

分数阶四神经元时滞递归神经网络的分岔。

Bifurcations of a Fractional-Order Four-Neuron Recurrent Neural Network with Multiple Delays.

机构信息

School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China.

Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan 653100, China.

出版信息

Comput Intell Neurosci. 2022 Sep 29;2022:1779582. doi: 10.1155/2022/1779582. eCollection 2022.

DOI:10.1155/2022/1779582
PMID:36210995
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9536962/
Abstract

This paper investigates the bifurcation issue of fractional-order four-neuron recurrent neural network with multiple delays. First, the stability and Hopf bifurcation of the system are studied by analyzing the associated characteristic equations. It is shown that the dynamics of delayed fractional-order neural networks not only depend heavily on the communication delay but also significantly affects the applications with different delays. Second, we numerically demonstrate the effect of the order on the Hopf bifurcation. Two numerical examples illustrate the validity of the theoretical results at the end.

摘要

本文研究了具有多个时滞的分数阶四神经元递归神经网络的分岔问题。首先，通过分析相关特征方程研究了系统的稳定性和 Hopf 分岔。结果表明，时滞分数阶神经网络的动力学不仅严重依赖于通信延迟，而且对不同延迟的应用也有显著影响。其次，我们数值研究了阶数对 Hopf 分岔的影响。最后通过两个数值例子验证了理论结果的有效性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/b2162e9de272/CIN2022-1779582.010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/6c837adabb66/CIN2022-1779582.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/f9e69cf1fcf6/CIN2022-1779582.002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/ffd3adb7ad46/CIN2022-1779582.003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/13dbb3ca08f2/CIN2022-1779582.004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/7ee840a69859/CIN2022-1779582.005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/7f9ce3fb01f1/CIN2022-1779582.006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/f6e99e0d9db4/CIN2022-1779582.007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/2b08228ae019/CIN2022-1779582.008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/501562f01f96/CIN2022-1779582.009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/b2162e9de272/CIN2022-1779582.010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/6c837adabb66/CIN2022-1779582.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/f9e69cf1fcf6/CIN2022-1779582.002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/ffd3adb7ad46/CIN2022-1779582.003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/13dbb3ca08f2/CIN2022-1779582.004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/7ee840a69859/CIN2022-1779582.005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/7f9ce3fb01f1/CIN2022-1779582.006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/f6e99e0d9db4/CIN2022-1779582.007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/2b08228ae019/CIN2022-1779582.008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/501562f01f96/CIN2022-1779582.009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a105/9536962/b2162e9de272/CIN2022-1779582.010.jpg

相似文献

1
Bifurcations of a Fractional-Order Four-Neuron Recurrent Neural Network with Multiple Delays.分数阶四神经元时滞递归神经网络的分岔。
Comput Intell Neurosci. 2022 Sep 29;2022:1779582. doi: 10.1155/2022/1779582. eCollection 2022.
2
Bifurcations in a fractional-order BAM neural network with four different delays.具有四种不同时滞的分数阶双向联想记忆神经网络中的分岔
Neural Netw. 2021 Sep;141:344-354. doi: 10.1016/j.neunet.2021.04.005. Epub 2021 Apr 18.
3
Bifurcations in a fractional-order neural network with multiple leakage delays.具有多个泄漏时滞的分数阶神经网络中的分岔。
Neural Netw. 2020 Nov;131:115-126. doi: 10.1016/j.neunet.2020.07.015. Epub 2020 Jul 18.
4
Dynamics of complex-valued fractional-order neural networks.复值分数阶神经网络的动力学
Neural Netw. 2017 May;89:39-49. doi: 10.1016/j.neunet.2017.02.011. Epub 2017 Mar 6.
5
Hopf bifurcation of an (n + 1) -neuron bidirectional associative memory neural network model with delays.时滞(n+1)神经元双向联想记忆神经网络模型的Hopf 分支。
IEEE Trans Neural Netw Learn Syst. 2013 Jan;24(1):118-32. doi: 10.1109/TNNLS.2012.2224123.
6
Effects of double delays on bifurcation for a fractional-order neural network.分数阶神经网络中双延迟对分岔的影响。
Cogn Neurodyn. 2022 Oct;16(5):1189-1201. doi: 10.1007/s11571-021-09762-2. Epub 2022 Jan 12.
7
Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays.具有多个时滞的分数阶Cohen-Grossberg神经网络中分歧的检测
Cogn Neurodyn. 2024 Jun;18(3):1379-1396. doi: 10.1007/s11571-023-09934-2. Epub 2023 Feb 28.
8
Qualitative Analysis and Bifurcation in a Neuron System With Memristor Characteristics and Time Delay.具有忆阻特性和时滞的神经元系统的定性分析和分岔。
IEEE Trans Neural Netw Learn Syst. 2021 May;32(5):1974-1988. doi: 10.1109/TNNLS.2020.2995631. Epub 2021 May 3.
9
Impact of leakage delay on bifurcation in high-order fractional BAM neural networks.高阶分数阶 BAM 神经网络中漏流延迟对分岔的影响。
Neural Netw. 2018 Feb;98:223-235. doi: 10.1016/j.neunet.2017.11.020. Epub 2017 Dec 6.
10
Stability and Hopf bifurcation analysis of a fractional-order ring-hub structure neural network with delays under parameters delay feedback control.参数延迟反馈控制下具有时滞的分数阶环-枢纽结构神经网络的稳定性与Hopf分岔分析
Math Biosci Eng. 2023 Nov 3;20(11):20093-20115. doi: 10.3934/mbe.2023890.

本文引用的文献

1
Synchronization of recurrent neural networks with unbounded delays and time-varying coefficients via generalized differential inequalities.基于广义微分不等式的具有无界时滞和时变系数的递归神经网络同步。
Neural Netw. 2021 Nov;143:161-170. doi: 10.1016/j.neunet.2021.05.022. Epub 2021 Jun 8.
2
Multistability of delayed fractional-order competitive neural networks.时滞分数阶竞争神经网络的多稳定性。
Neural Netw. 2021 Aug;140:325-335. doi: 10.1016/j.neunet.2021.03.036. Epub 2021 Apr 8.
3
Undamped Oscillations Generated by Hopf Bifurcations in Fractional-Order Recurrent Neural Networks With Caputo Derivative.
分数阶递归神经网络中具有 Caputo 导数的 Hopf 分支产生的无阻尼振荡。
IEEE Trans Neural Netw Learn Syst. 2015 Dec;26(12):3201-14. doi: 10.1109/TNNLS.2015.2425734. Epub 2015 May 14.
4
Distributed coordination of networked fractional-order systems.网络化分数阶系统的分布式协调
IEEE Trans Syst Man Cybern B Cybern. 2010 Apr;40(2):362-70. doi: 10.1109/TSMCB.2009.2024647. Epub 2009 Jul 7.
5
An evolutionary algorithm that constructs recurrent neural networks.一种构建递归神经网络的进化算法。
IEEE Trans Neural Netw. 1994;5(1):54-65. doi: 10.1109/72.265960.
6
Exponential synchronization of a class of neural networks with time-varying delays.一类具有时变延迟的神经网络的指数同步
IEEE Trans Syst Man Cybern B Cybern. 2006 Feb;36(1):209-15. doi: 10.1109/tsmcb.2005.856144.
7
A recurrent network mechanism of time integration in perceptual decisions.感知决策中时间整合的循环网络机制。
J Neurosci. 2006 Jan 25;26(4):1314-28. doi: 10.1523/JNEUROSCI.3733-05.2006.
8
Statistical mechanics beyond the Hopfield model: solvable problems in neural network theory.超越霍普菲尔德模型的统计力学：神经网络理论中的可解问题。
Rev Neurosci. 2003;14(1-2):181-93. doi: 10.1515/revneuro.2003.14.1-2.181.
9
Neurons with graded response have collective computational properties like those of two-state neurons.具有分级反应的神经元具有与双态神经元类似的集体计算特性。
Proc Natl Acad Sci U S A. 1984 May;81(10):3088-92. doi: 10.1073/pnas.81.10.3088.