具时滞的联想记忆神经网络模型动力学性质

李秀玲

具时滞的联想记忆神经网络模型动力学性质

李秀玲

吉林财经大学应用数学学院, 长春 130117

基金项目: 国家自然科学基金资助项目(10671031)

详细信息

作者简介:
李秀玲(1973-),女,吉林长春人,副教授,xlli2003@yahoo.com.cn.

中图分类号: TP183
计量
- 文章访问数: 1381
- HTML全文浏览量: 57
- PDF下载量: 622
- 被引次数: 0
出版历程
- 收稿日期: 2012-03-19
- 网络出版日期: 2013-03-31

Dynamical quality in bidirectional associative memory neural network model

Li Xiuling

College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China

摘要

摘要: 为了研究时滞对联想记忆神经网络模型动力学行为的影响,考虑了一个含有n+1个神经元的具多时滞的双向联想记忆神经网络模型.以模型中的时滞为参数,利用泛函微分方程的全局Hopf分支存在定理和常微分方程的Bendixson周期解不存在定理,给出该模型非平凡周期解全局存在的充分条件,为双向联想记忆神经网络的设计和应用提供了重要的理论依据.最后利用一个例子进行了数值仿真,仿真结果表明了结论的有效性.
- 双向联想记忆神经网络 /
- 时滞 /
- 周期解 /
- 动力学性质
Abstract: In order to study for the effect of delay in dynamic behavior of associative memory neural network model, an n+1-dimensional bidirectional associative memory (BAM) neural network model with multi-delay was considered. Sufficient conditions for nontrivial periodic solution were met by the model by taking delay as a parameter, using the global Hopf bifurcation existence theorem of the functional differential equation and the Bendixson non-existent theorem of the ordinary differential equation. These provide important theoretical basis for the design and application of BAM neural network. Finally, numerical simulations were carried out and results show that the proposed conclusion is effective.
- bidirectional associative memory neural network /
- time delay /
- periodic solutions /
- dynamical quality

HTML全文

参考文献(1)

[1] Xiang Hongjun,Cao Jinde.Almost periodic solution of Cohen-Grossberg neural networks with bounded and unbounded delays[J].Nonlinear Analysis:Real World Applications,2009,10:2407-2419 [2] 吴然超.时滞离散神经网络的同步控制[J].物理学报,2009,58:139-142 Wu Ranchao.Synchronization of delayed discrete-time neural networks[J].Acta Physica Sinica,2009,58:139-142(in Chinese) [3] 刘开宇,王成亮.非线性二元离散神经网络模型的渐近性[J].湖南大学学报:自然科学版,2010,37:53-56 Liu Kaiyu,Wang Chengliang.Asymptotic behaviors for a class of nonlinear discrete-time neural networks with two neurons[J].Journal of Hunan University:Natural Sciences,2010,37:53-56(in Chinese) [4] 戴娟,周宗福.具S-型分布时滞的模糊细胞神经网络的周期解及指数稳定性[J].数学的实践与认识,2009,39:118-128 Dai Juan,Zhou Zongfu.Periodic solutions and exponential stability to fuzzy cellular neural networks with S-type distributed delays[J].Mathematics in Practice and Theory,2009,39:118-128(in Chinese) [5] 李清华,吴春雪,时宝.脉冲时滞细胞神经网络的周期解的存在性[J].数学的实践与认识,2010,40:115-123 Li Qinghua,Wu Chunxue,Shi Bao.Existence of periodic solutions of impulsive delay cellular neural networks[J].Mathematics in Practice and Theory,2010,40:115-123(in Chinese) [6] Fan Meng,Zou Xingfu.Global asymptotic stability of a class of nonautonomous integro-differential systems and applications[J].Nonlinear Analysis TMA,2004,57:111-135 [7] Kosko B.Bidirectional associative memories[J].IEEE Trans Syst Man Cybernet,1988,18:49-60 [8] 李永昆.具时滞和脉冲的BAM神经网络的稳定性研究[J].科学观察,2010,5:54-55 Li Yongkun.Stability study on BAM neural network with delay and pulse[J].Science Focus,2010,5:54-55(in Chinese) [9] Song Y,Han M,Wei J.Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays[J].Physica D:Nonlinear Phenomena,2005,200:185-204 [10] 张明明,张春蕊.时滞BAM神经网络模型的稳定性分析[J].生物数学学报,2008,23:257-264 Zhang Mingming,Zhang Chunrui.Stability analysis on BAM neural network model with multi-delays[J].Journal of Biomathematics,2008,23:257-264(in Chinese) [11] Li M Y,Muldowney J.On Bendixson's criterion[J].J Diff Eqs,1994,106:27-39 [12] Wu J.Symmetric functional differential equations and neural networks with memory[J].Tran Amer Math Soc,1998,350:4799-4838 [13] 李秀玲.具时滞的四维神经网络模型的分支问题研究[D].长春:东北师范大学,2005 Li Xiuling.The research on the bifurcation of a four-dime neural model with delays[D].Changchun:Northeast Normal University,2005(in Chinese)

施引文献

资源附件(0)

访问统计