基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

王利敏; 宋乾坤; 赵振江

doi:10.21656/1000-0887.370221

基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

doi: 10.21656/1000-0887.370221

¹重庆交通大学信息科学与工程学院, 重庆 400074;²重庆交通大学数学系, 重庆 400074;³湖州师范学院数学系, 浙江湖州 313000

基金项目: 国家自然科学基金(61273021;61473332); 重庆市研究生科研创新项目(CYS16179)

详细信息

作者简介:
王利敏(1993—)，女，硕士生(E-mail: liminwangm@163.com);宋乾坤(1963—)，男，教授，博士(通讯作者. E-mail: qiankunsong@163.com);赵振江(1961—)，男，教授，硕士(E-mail: zhaozjcn@163.com).

中图分类号: O175.13
计量
- 文章访问数: 1523
- HTML全文浏览量: 249
- PDF下载量: 1056
- 被引次数: 0
出版历程
- 收稿日期: 2016-07-19
- 修回日期: 2016-11-09
- 刊出日期: 2017-03-15

Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays

¹School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;³Department of Mathematics, Huzhou Teachers University, Huzhou, Zhejiang 313000, P.R.China

Funds: The National Natural Science Foundation of China(61273021; 61473332)

摘要

摘要: 研究了分数阶复值神经网络的稳定性.针对一类基于忆阻的分数阶时滞复值神经网络,利用Caputo分数阶微分意义上Filippov解的概念, 研究其平衡点的存在性和唯一性.采用了将复值神经网络分离成实部和虚部的研究方法, 将实数域上的比较原理、不动点定理应用到稳定性分析中, 得到了模型平衡点存在性、唯一性和全局渐近稳定性的充分判据.数值仿真实例验证了获得结果的有效性.
- 复值神经网络 /
- 分数阶微积分 /
- 忆阻器 /
- Filippov解 /
- 全局渐近稳定性
Abstract: The global stability of fractional-order complex-valued neural networks was investigated. For a class of memristor-based fractional-order complex-valued neural networks with time delays, under the concept of the Filippov solution in the sense of Caputo’s fractional derivation, the existence and uniqueness of the equilibrium point were discussed. The comparison principle and the fixed-point theorem were applied to the stability analysis through division of the complex values into the real part and the imaginary part. Some sufficient criteria for the global asymptotic stability of memristor-based fractional-order complex-valued neural networks were derived. Finally, a simulation example shows the effectiveness of the obtained results.
- complex-valued neural network /
- fractional calculus /
- memristor /
- Filippov solution /
- global asymptotic stability

HTML全文

参考文献(25)

[1]	Kilbas A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations [M]. New York: Elsevier Science Inc, 2006.
[2]	Boroomand A, Menhaj M B. Fractional-Order Hopfield Neural Networks [M]//Advances in Neuro-Information Processing. Berlin, Heidelberg: Springer, 2009: 883-890.
[3]	Ahmeda E, Elgazzar A S. On fractional order differential equations model for nonlocal epidemics[J]. Physica A: Statistical Mechanics and Its Applications,2007,379(2): 607-614.
[4]	Diethelm K, Ford N J. Analysis of fractional differential equations[J]. Journal of Mathematical Analysis and Applications,2002,265(2): 229-248.
[5]	YANG Xu-jun, SONG Qian-kun, LIU Yu-rong, et al. Finite-time stability analysis of fractional-order neural networks with delay[J]. Neurocomputing,2015,152: 19-26.
[6]	ZHANG Shuo, YU Yong-guang, WANG Qing. Stability analysis of fractional-order Hopfield neural networks with discontinuous activation functions[J]. Neurocomputing,2016,171: 1075-1084.
[7]	Rakkiyappan R, CAO Jin-de, Velmurugan G. Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2015,26: 84-97.
[8]	Chua L. Memristor-the missing circuit element[J]. IEEE Transactions on Circuit Theory,1971,18(5): 507-519.
[9]	HU Jin, WANG Jun. Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays[C]//The 2010 International Joint Conference on Neural Networks.2010: 1-8.
[10]	WU Ai-long, WEN Shi-ping, ZENG Zhi-gang. Synchronization control of a class of memristor-based recurrent neural networks[J]. Information Sciences,2012,183: 106-116.
[11]	BAO Hai-bo, Park Ju H, CAO Jin-de. Adaptive synchronization of fractional-order memristor-based neural networks with time delay[J]. Nonlinear Dynamics,2015,82(3): 1343-1354.
[12]	Velmurugan G, Rakkiyappan R, CAO Jin-de. Finite-time synchronization of fractional-order memristorbased neural networks with time delays[J]. Neural Networks,2016,73: 36-46.
[13]	CHEN Li-ping, WU Ran-chao, CAO Jin-de, et al. Stability and synchronization of memristor-based fractional-order delayed neural networks[J]. Neural Networks,2015,71: 37-44.
[14]	Hirose A. Dynamics of fully complex-valued neural networks[J]. Electronics Letters,1992,28: 1492-1494.
[15]	Nitta T. An analysis of the fundamental structure of complex-valued neurons[J]. Neural Processing Letters,2000,12(3): 239-246.
[16]	HU Jin, WANG Jun. Global stability of complex-valued recurrent neural networks with time-delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2012,23(6): 853-865.
[17]	ZHOU Bo, SONG Qian-kun. Boundedness and complete stability of complex-valued neural networks with time delay[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(8): 1227-1238.
[18]	ZHANG Zi-ye, LIN Chong, CHEN Bing. Global stability criterion for delayed complex-valued recurrent neural networks[J]. IEEE Transactions on Neural Networks and Learning Systems,2014,25: 1704-1708.
[19]	SONG Qian-kun, ZHAO Zhen-jiang. Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales[J]. Neurocomputing,2016,171: 179-184.
[20]	HU Shou-chuan. Differential equations with discontinuous right-hand sides[J]. Journal of Mathematical Analysis and Applications, 1991,154(2): 377-390.
[21]	ZHANG Guo-dong, SHEN Yi, SUN Jun-wei. Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays[J]. Nonlinear Analysis:Hybrid Systems,2012,97: 149-154.
[22]	ZHANG Shuo, YU Yong-guang, WANG Hu. Mittag-Leffler stability of fractional-order Hopfield neural networks[J]. Nonlinear Analysis: Hybrid Systems, 2015,16: 104-121.
[23]	WANG Hu, YU Yong-guang, WEN Guo-guang, et al. Global stability analysis of fractional-order Hopfield neural networks with time delay[J]. Neurocomputing,2015,154: 15-23.
[24]	DENG Wei-hua, LI Chang-pin, LU Jin-hu, et al. Stability analysis of linear fractional differential system with multiple time delays[J]. Nonlinear Dynamics,2007,48(4): 409-416.
[25]	CHEN Jie-jie, ZENG Zhi-gang, JIANG Ping. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51: 1-8.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1523
HTML全文浏览量: 249
PDF下载量: 1056
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

doi: 10.21656/1000-0887.370221

作者简介:
王利敏(1993—)，女，硕士生(E-mail: liminwangm@163.com);宋乾坤(1963—)，男，教授，博士(通讯作者. E-mail: qiankunsong@163.com);赵振江(1961—)，男，教授，硕士(E-mail: zhaozjcn@163.com).

计量

Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays

计量

目录

留言板

基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

doi: 10.21656/1000-0887.370221

作者简介: 王利敏(1993—)，女，硕士生(E-mail: liminwangm@163.com);宋乾坤(1963—)，男，教授，博士(通讯作者. E-mail: qiankunsong@163.com);赵振江(1961—)，男，教授，硕士(E-mail: zhaozjcn@163.com).

计量

出版历程

Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays

计量

出版历程

目录

作者简介:
王利敏(1993—)，女，硕士生(E-mail: liminwangm@163.com);宋乾坤(1963—)，男，教授，博士(通讯作者. E-mail: qiankunsong@163.com);赵振江(1961—)，男，教授，硕士(E-mail: zhaozjcn@163.com).