期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
时标上的 Clifford 值概周期函数与动力方程的 Clifford 值概周期解
- (云南大学 数学与统计学院，云南 昆明 650091)
-
DOI：10.13763/j.cnki.jhebnu.nse.202401001
Clifford Valued Almost Periodic Functions on Time Scales and Clifford Valued Almost Periodic Solutions of Dynamic Equations
摘要/Abstract
为了更好地在时标上探讨 Clifford 值神经网络概周期解的存在性,首先,从周期时标的定义出发,利用 Clifford 代数空间的完备性,给出时标上 Clifford 值概周期函数的定义,并讨论了这类函数的相关性质.其次,通过证明时标上 Clifford 值右稠密连续函数空间的完备性,以及时标上 Clifford 值概周期函数空间是时标上 Clifford 值右稠密连续函数空间的闭子空间,获得时标上 Clifford 值概周期函数空间的完备性.最后,利用时标上 Clifford 值概周期函数相关性质,得到一阶动力方程 Clifford 值概周期解的存在性定理.
In order to discuss the existence and stability of almost periodic solutions of Clifford-valued neural networks on time scales,firstly,the definition of Clifford valued almost periodic functions on time scales is given based on the definition of periodic time scales and the completeness of Clifford algebraic space,and the related properties of these functions are discussed.Secondly,the completeness of Clifford valued almost periodic functions space on time scales is obtained by proving that the space of Clifford valued right dense continuous functions on time scales is complete and that the space of Clifford valued almost periodic functions on time scales is a closed subspace of the space of Clifford valued right dense continuous functions on time scales.Finally,by using the properties of Clifford value almost periodic function on time scale,the existence theorem of Clifford value almost periodic solution of the first order dynamic equation is obtained.
关键词
参考文献 18
- [1] 周立群,宋协慧.一类具比例时滞脉冲递归神经网络的全局多项式稳定性[J].电子科技大学学报,2021,50(1):91-100.doi:10.12178/1001-0548.2019171 ZHOULiqun,SONGXiehui.Global Polynomial Stability of a Class of Impulsive Recurrent Neural Networks with Propor-tional[J].Journal of University of Electronic Science and Technology of China,2021,50(1):91-100.
- [2] 刘新,陈丽丽,黄帅.一类随机细胞神经网络的均方指数稳定性[J].哈尔滨理工大学学报,2020,25(5):149-157.doi:10.15938/j.jhust.2020.05.021 LIUXin,CHENLili,HUANGShuai.Mean Square Exponential Stability of a Class of Stochastic Cellular Neural Net-works[J].Journal of Harbin University of Science and Technology,2020,25(5):149-157.
- [3] 宋协慧,周立群.一类具多比例时滞脉冲递归神经网络的稳定性分析[J].天津师范大学学报(自然科学版),2020,40(5):1-8.doi:10.19638/j.issn1671-1114.20200501 SONG Xiehui,ZHOU Liqun.Stability Analysis of a Class of Impulsive Recurrent Neural Networks with Multi-proportion- Al Delays[J].Journal of Tianjin Normal University (NaturalScienceEdition),2020,40(5):1-8.
- [4] 刘锦,赵维锐.具有时变时滞的中立型神经网络的稳定性分析[J].华东师范大学学报(自然科学版),2020(4):35-44.doi:10.3969/j.issn.1000-5641.201911016 LIU Jin,ZHAO Weirui.Stability Analysis of Neutral Neural Networks with Time-varying Delays[J].Journal East China Normal University (NaturalScience),2020(4):35-44.
- [5] 徐西睿.改进神经网络的舰船电力系统稳定性容错控制[J].船舰科学技术,2020,42(14):115-117.doi:10.3404/j.issn. 1672-7649.2020.7A.039 XU Xirui.Fault Tolerant Control of Ship Power System Stability Based on Improved Neural Network[J].Ship Science and Technology,2020,42(14):115-117.
- [6] NITTA T.Solving the XOR Problem and The Detection of Symmetry Using a Single Complex-valued Neuron[J].Neural Networks,2003,16(8):1101-1105.doi:10.1016/S0893-6080(3)00168-0
- [7] 方聪娜,宾红华.具有时变时滞的复值神经网络的概周期解[J].厦门大学学报(自然科学版),2021,60(6):989-995.doi:10.6043/j.issn.0438-0479.201909036 FANG Congna,BIN Honghua.The Almost Periodic Solution of Complex-valued Neural Networks with Time-varying De-lays[J].Journal of Xiamen University(NaturalScience),2021,60(6):989-995.
- [8] 冯靓,胡成,于娟.脉冲耦合复值神经网络的全局渐进同步[J].西南师范大学学报(自然科学版),2022,47(3):9-15.doi:10.13718/j.cnki.xsxb.2022.03.002 FENG Liang,HU Cheng,YU Juan.On Global Asymptotic Synchronization of Impulsively Coupled Neural Networks with Complex Values[J].Journal Southwest China Normal University (NaturalScienceEdition),2022,47(3):9-15.
- [9] 陈宇,周博,宋乾坤.具有不确定性的分数阶时滞复值神经网络无源性[J].应用数学和力学,2021,42(5):492-499.doi:10.21656/1000-0887.410309 CHEN Yu,ZHOU Bo,SONG Qiankun.Passivity of Fractional-order Delayed Complex-valued Neural Networks withUn-certainties[J].Applied Mathematics and Mechanics,2021,42(5):492-499.
- [10] 刘苑醒,张玮玮,张红梅.分数阶复值时滞神经网络的准一致同步[J].安庆师范大学学报(自然科学版),2020,26(3):6-15.doi:10.13757/j.cnki.cn34-1328/n.2020.03.002 LIU Yuanxing,ZHANG Weiwei,ZHANG Hongmei.Quasi-uniform Synchronization of Fractional-order Complex-valued Neural Networks with Time Delay[J].Journal of an Qing Normal University (NaturalScienceEdition),2020,26(3):6-15.
- [11] 舒含奇,宋乾坤.带有时滞的Clifford值神经网络的全局指数稳定性[J].应用数学和力学,2017,38(5):513-525.doi:10.21656/1000-0887.370319 SHU Hanqi,SONG Qiankun.Global Stability of Clifford-valued Recurrent Neural Networks with Mixed Time-varying Delays[J].AppliedMathematicsandMechanics,2017,38(5):513-525.
- [12] 姜海洋.Clifford代数值耦合系统网络稳定性与同步性的研究[D].黑龙江:哈尔滨工业大学,2022.doi:10.27061/d.cnki.ghgdu.2019.003380 JIANG Haiyang.Study of Stability and Synchronization for Clifford-valued Coupled System on Network[D].Heilong River:HarbinInstituteofTechnology,2022.
- [13] BOHNER M,PETERSON A.Dynamic Equations on Time Scales:An Introduction with Applications[M].Boston: Birkhauser,2001.
- [14] WANG C,AGARWAL R P,O'REGAN D,SAKTHIVEL R.Theory of Translation Closedness for Time Scales with Ap-plications in Translation Functions and Dynamic Equations[M]. Swizerland: Springer Nature Switzerland AG,2020.doi:10.1007/978-3-030-38644-3
- [15] 华亮,黄宇,丁立军,等.Clifford代数空间上的三维多模医学图像配准[J].光电工程,2014,41(1):65-72.doi:10.3969/j.issn.1003-501X.2014.01.012 HUA Liang,HUANG Yu,DING Lijun,etal.Multimodality 3D Medical Image Registration in Clifford Algebra Space[J].Opto-electronic Engineering,2014,41(1):65-72.
- [16] 宋元凤,李武明,杨柳.实Clifford代数的矩阵表示[J].东北师大学报(自然科学版),2019,51(1):9-12.doi:10.16163/j.cnki..22-1123/n.2019.01.003 SONG Yuanfeng,LI Wuming,YANG Liu.Matrix Representations of Real Clifford Algebras[J].Journal of Northeast Normal University(NaturalScienceEdition),2019,51(1):9-12.
- [17] 王瑞,金林波,陶磊,等.基于Clifford代数的3D点云模型数字水印算法[J].上海交通大学学报,2013,47(12):1863-1869.doi:10.16183/j.cnki.jsjtu.2013.12.009 WANG Rui,JIN Linbo,TAO Lei,etal.Digital Watermarking Algorithm for 3D Point Cloud Model Based onCliffordAl-gebra[J].Journal of Shanghai JiaoTong University,2013,47(12):1863-1869.
- [18] LEVITSAN B M,ZHIKOV V V.Almost Periodic Functions and Functional Differential Equations[M]. Cambridge:Cam-bridgeUniversityPress,1982.