您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (10): 67-74.doi: 10.6040/j.issn.1671-9352.0.2023.157

•   • 上一篇    下一篇

具有Dirichlet有界条件的反应扩散Cohen-Grossberg神经网络指数稳定性

李蕾1,2(),叶永升2,*()   

  1. 1. 河海大学数学学院，江苏 南京 211100
    2. 淮北师范大学数学科学学院，安徽 淮北 235000
  • 收稿日期:2023-04-16 出版日期:2023-10-20 发布日期:2023-10-17
  • 通讯作者: 叶永升 E-mail:llei0910@163.com;yeys@chnu.edu.cn
  • 作者简介:李蕾(1993—), 女, 博士，研究方向为神经网络与多智能体的控制. E-mail：llei0910@163.com
  • 基金资助:
    国家自然科学基金资助项目(12071188);安徽省高校自然科学研究项目(KJ2021B04)

Exponential stability of reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions

Lei LI1,2(),Yongsheng YE2,*()   

  1. 1. School of Mathematics, Hohai University, Nanjing 211100, Jiangsu, China
    2. College of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China
  • Received:2023-04-16 Online:2023-10-20 Published:2023-10-17
  • Contact: Yongsheng YE E-mail:llei0910@163.com;yeys@chnu.edu.cn

RichHTML

2

PDF (PC)

416

摘要：

通过构造合适的Lyapunov泛函并结合数学分析技巧，讨论一类具有Dirichlet边界条件的基于马尔可夫切换的脉冲时滞反应扩散Cohen-Grossberg神经网络模型的指数稳定性。利用不等式技术和随机分析理论，得到了神经网络的指数稳定的若干充分判据。最后通过算例验证了所得到结果的有效性。

关键词: 马尔可夫切换, 脉冲, 时滞, 反应扩散神经网络, 指数稳定

Abstract:

By constructing a suitable Lyapunov functional and combining it with mathematical analysis techniques, we discuss the exponential stability of impulsive time delay reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions and Markovian switching. Some sufficient criteria for exponential stability of neural networks are obtained by using the inequality technique and stochastic analysis theory. Finally, an example is given to verify the validity of the results.

Key words: Markovian switching, impulsive, time delay, reaction-diffusion neural network, exponential stability

中图分类号: 

  • O175

图1

系统(3)的轨迹仿真结果"

1 CHUA L O , YANG L . Cellular neural networks: applications[J]. IEEE Transactions on Biomedical Circuits and Systems, 1988, 35 (10): 1273- 1290.
doi: 10.1109/31.7601
2 ZENG Z G , WANG J . Design and analysis of high-capacity associative memories based on a class of discrete-time recurrent neural networks[J]. IEEE Transactions on Systems Man Cybernetics, Part B: Cybernetics, 2008, 38 (6): 1525- 1536.
doi: 10.1109/TSMCB.2008.927717
3 LIU Q S , WANG J . A projection neural network for constrained quadratic minimax optimization[J]. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26 (11): 2891- 2900.
doi: 10.1109/TNNLS.2015.2425301
4 CAO J D , WANG J . Global asymptotic stability of a general class of recurrent neural networks with time-varying delays[J]. IEEE Transactions on Circuits and Systems—I fundamental Theory Applications, 2003, 50 (1): 34- 44.
doi: 10.1109/TCSI.2002.807494
5 ZENG Z G , WANG J , LIAO X X . Global exponential stability of a general class of recurrent neural networks with time-varying delays[J]. IEEE Transactions on Systems Man Cybernetics, Part B: Cybernetics, 2003, 50 (10): 1353- 1358.
6 LIU P , ZENG Z G , WANG J . Multiple Mittag-Leffler stability of fractional-order recurrent neural networks[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 47 (8): 2279- 2288.
doi: 10.1109/TSMC.2017.2651059
7 WANG J L , QIN Z , WU H N , et al. Analysis and pinning control for output synchronization and H∞ output synchronization of multi-weighted complex networks[J]. IEEE Transactions on Cybernetics, 2019, 49 (4): 1314- 1326.
doi: 10.1109/TCYB.2018.2799969
8 WANG J L , XU M , WU H N , et al. Passivity analysis and pinning control of multi-weighted complex dynamical networks[J]. IEEE Transactions on Network Science and Engineering, 2019, 6 (1): 60- 73.
doi: 10.1109/TNSE.2017.2771267
9 WANG J L , WU H N , HUANG T W , et al. Passivity and output synchronization of complex dynamical networks with fixed and adaptive coupling strength[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29 (2): 364- 376.
doi: 10.1109/TNNLS.2016.2627083
10 HU C , JIANG H , TENG Z . Impulsive control and synchronization for delayed neural networks with reaction-diffusion terms[J]. IEEE Transactions on Neural Networks and Learning Systems, 2010, 21 (1): 67- 81.
doi: 10.1109/TNN.2009.2034318
11 CHEN W H , LUO S , ZHENG W X . Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption[J]. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27 (12): 2696- 2710.
doi: 10.1109/TNNLS.2015.2512849
12 ZHANG H , ZENG Z , HAN Q L . Synchronization of multiple reaction-diffusion neural networks with heterogeneous and unbounded time-varying delays[J]. IEEE Transactions on Cybernetics, 2019, 49 (8): 2980- 2991.
doi: 10.1109/TCYB.2018.2837090
13 LV Y , HU C , YU J , et al. Edge-based fractional order adaptive strategies for synchronization of fractional-order coupled networks with reaction-diffusion terms[J]. IEEE Transactions on Cybernetics, 2020, 50 (4): 1582- 1594.
doi: 10.1109/TCYB.2018.2879935
14 TU Z , DING N , LI L , et al. Adaptive synchronization of memristive neural networks with time-varying delays and reaction-diffusion term[J]. Applied Mathematics and Computation, 2017, 311, 118- 128.
doi: 10.1016/j.amc.2017.05.005
15 EVANS L C . Partial differential equation[M]. 2nd ed. Berkeley: American Mathematical Society, 1998.
16 CAO Y Y , CAO Y T , WEN S P , et al. Passivity analysis of delayed reaction-diffusion memristor-based neural networks[J]. Neural Networks, 2019, 109, 159- 167.
doi: 10.1016/j.neunet.2018.10.004
17 LI R X , CAO J D . Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term[J]. Applied Mathematics and Computation, 2016, 278, 54- 69.
doi: 10.1016/j.amc.2016.01.016
18 WU H Q , ZHANG X W , LI R X , et al. Adaptive anti-synchronization and H∞ anti-synchronization for memristive neural networks with mixed time delays and reaction-diffusion terms[J]. Neurocomputing, 2015, 168, 726- 740.
doi: 10.1016/j.neucom.2015.05.051
19 SHI G D , MA Q . Synchronization of stochastic Markovian jump neural networks with reaction-diffusion terms[J]. Neurocomputing, 2012, 77 (1): 275- 280.
doi: 10.1016/j.neucom.2011.08.024
20 ZHU Q X . pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching[J]. Journal of the Franklin Institute, 2014, 351 (7): 3965- 3986.
doi: 10.1016/j.jfranklin.2014.04.001
21 ZHU Q X . Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching[J]. International Journal of Control, 2017, 90 (8): 1703- 1712.
doi: 10.1080/00207179.2016.1219069
22 ZHANG Y , LUO Q . Novel stability criteria for impulsive delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincarè inequality[J]. Chaos, Solitons & Fractals, 2012, 45 (8): 1033- 1040.
23 LI X D , CAO J D . An impulsive delay inequality involving unbounded time varying delay and applications[J]. IEEE Transactions on Automatic Control, 2017, 62 (7): 3618- 3625.
doi: 10.1109/TAC.2017.2669580
24 WANG X , LI C D , HUANG T W . Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays[J]. Neural Networks, 2014, 60, 25- 32.
doi: 10.1016/j.neunet.2014.07.008
25 LU J G . Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions[J]. Chaos, Solitons and Fractals, 2008, 35 (1): 116- 125.
doi: 10.1016/j.chaos.2007.05.002
[1] 王雅迪,袁海龙. 时滞Lengyel-Epstein反应扩散系统的Hopf分支[J]. 《山东大学学报(理学版)》, 2023, 58(8): 92-103.
[2] 李莉,杨和. 二阶脉冲发展方程非局部问题mild解的存在性[J]. 《山东大学学报(理学版)》, 2023, 58(6): 57-67.
[3] 孙盼,张旭萍. 具有无穷时滞脉冲发展方程解的连续依赖性[J]. 《山东大学学报(理学版)》, 2023, 58(6): 77-83, 91.
[4] 许越,韩晓玲. 具有双时滞的媒体效应对西藏地区包虫病控制的影响[J]. 《山东大学学报(理学版)》, 2023, 58(5): 53-62.
[5] 郭改慧,王晶晶,李旺瑞. 一类具有时滞的植被-水反应扩散模型的Hopf分支[J]. 《山东大学学报(理学版)》, 2023, 58(10): 32-42, 53.
[6] 李永花,张存华. 具有Dirichlet边界条件的单种群时滞反应扩散模型的稳定性[J]. 《山东大学学报(理学版)》, 2023, 58(10): 122-126.
[7] 庞玉婷,赵东霞,鲍芳霞. 具有多时滞和多参数的双向环状网络的稳定性[J]. 《山东大学学报(理学版)》, 2022, 57(8): 103-110.
[8] 王苗苗,丁小丽,李佳敏. 分数阶随机时滞微分方程的波形松弛方法[J]. 《山东大学学报(理学版)》, 2022, 57(1): 101-110.
[9] 沈维,张存华. 时滞食饵-捕食系统的多次稳定性切换和Hopf分支[J]. 《山东大学学报(理学版)》, 2022, 57(1): 42-49.
[10] 原田娇,李强. 一类脉冲发展方程IS-渐近周期mild解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(6): 10-21.
[11] 魏立祥,张建刚,南梦冉,张美娇. 具有时滞的磁通神经元模型的稳定性及Hopf分岔[J]. 《山东大学学报(理学版)》, 2021, 56(5): 12-22.
[12] 马维凤,陈鹏玉. 状态依赖型时滞微分方程的解流形及其C1-光滑性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 92-96.
[13] 马德青,胡劲松. 消费者参考质量存在时滞效应的动态质量改进策略[J]. 《山东大学学报(理学版)》, 2020, 55(9): 101-89.
[14] 章欢,李永祥. 含时滞导数项的高阶常微分方程的正周期解[J]. 《山东大学学报(理学版)》, 2019, 54(4): 29-36.
[15] 张申贵. 变分方法对变指数脉冲微分系统的应用[J]. 《山东大学学报(理学版)》, 2019, 54(4): 22-28.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 罗斯特,卢丽倩,崔若飞,周伟伟,李增勇*. Monte-Carlo仿真酒精特征波长光子在皮肤中的传输规律及光纤探头设计[J]. J4, 2013, 48(1): 46 -50 .
[2] 田学刚, 王少英. 算子方程AXB=C的解[J]. J4, 2010, 45(6): 74 -80 .
[3] 霍玉洪,季全宝. 一类生物细胞系统钙离子振荡行为的同步研究[J]. J4, 2010, 45(6): 105 -110 .
[4] 杨伦，徐正刚，王慧*，陈其美，陈伟，胡艳霞，石元，祝洪磊，曾勇庆*. RNA干扰沉默PID1基因在C2C12细胞中表达的研究[J]. J4, 2013, 48(1): 36 -42 .
[5] 刘婷婷,陈志勇,李晓琴*,杨文志. 随机变量序列的Berry-Esseen界[J]. 山东大学学报（理学版）, 2014, 49(03): 101 -106 .
[6] 刘艳萍,吴群英. 优化权重下高斯序列最大值几乎处处中心极限定理[J]. 山东大学学报（理学版）, 2014, 49(05): 50 -53 .
[7] 赵君1,赵晶2,樊廷俊1*,袁文鹏1,3,张铮1,丛日山1. 水溶性海星皂苷的分离纯化及其抗肿瘤活性研究[J]. J4, 2013, 48(1): 30 -35 .
[8] 杨永伟1,2,贺鹏飞2,李毅君2,3. BL-代数的严格滤子[J]. 山东大学学报（理学版）, 2014, 49(03): 63 -67 .
[9] 李敏1,2,李歧强1. 不确定奇异时滞系统的观测器型滑模控制器[J]. 山东大学学报（理学版）, 2014, 49(03): 37 -42 .
[10] 杨军. 金属基纳米材料表征和纳米结构调控[J]. 山东大学学报（理学版）, 2013, 48(1): 1 -22 .
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发