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)》 ›› 2019, Vol. 54 ›› Issue (10): 97-108.doi: 10.6040/j.issn.1671-9352.0.2018.600

• • 上一篇    

时标上具有联接项时滞的分流抑制细胞神经网络的概自守解

戴丽华,惠远先*   

  1. 普洱学院数学与统计学院, 云南 普洱 665000
  • 发布日期:2019-10-12
  • 作者简介:戴丽华(1991— ),女,硕士,助教,研究方向为微分方程定性理论. E-mail:hlm2136816@163.com*通信作者简介:惠远先(1983— ),男,博士,讲师,研究方向为微分方程定性理论、生物数学. E-mail:huiyuanxian1983@126.com
  • 基金资助:
    云南省教育厅基金资助项目(2018JS517)

Almost automorphic solutions for shunting inhibitory cellular neural networks with leakage delays on time scales

DAI Li-hua, HUI Yuan-xian*   

  1. School of Mathematics and Statistics, Puer University, Puer 665000, Yunnan, China
  • Published:2019-10-12

摘要: 提出时标上带联结项时变时滞和连续分布时滞的分流抑制细胞神经网络模型,通过运用时标上线性动力方程的指数二分法和不动点定理,获得所研究模型的概自守解全局指数稳定的充分条件。最后,给出具体例子说明所得结论的有效性。

关键词: 概自守解, 时标, 分流抑制细胞神经网络, 全局指数稳定

Abstract: Shunting inhibitory cellular neural networks(SICNNs)with time-varying delays in the leakage term and continuously distributed delays on time scale T is proposed. Based on the exponential dichotomy of linear dynamic equation on time scales, fixed point theorems on time scales, we obtain some new sufficient conditions for the existence a global exponential stability of almost automorphic solution for the class of neural networks. Moreover, we give convictive numerical examples to show the feasibility of our results. This paper contains the several classes of functional differential equations, including the existence of solutions and the stability of this solution on time scales. Also, some new results are obtained.

Key words: almost automorphic solution, time scale, shunting inhibitory neural network, global exponential stability

中图分类号: 

  • O193
[1] MCCULLOCCH W S, PITTS W A. Logical calculus of the ideas immanent in nervous activity[J]. Bulletin of Mathematical Biophysics, 1943, 5:115-133.
[2] HOPFIELD J J. Neural network and physical system with emergent collective computational abilities[J]. Proceedings of the National Academy of Sciences, 1982, 79(8):2554-2558.
[3] HOPFIELD J J. Neurons with graded response have collective computational properties like those of two-stage neurons[J]. Proceedings of the National Academy of Sciences, 1984, 81(10):3088-3092.
[4] BOUZERDOUM A, PINTER P B. Analysis and analog implementaion of directionally sensitive shunting inhibitory neural networks[J]. Proceedings of the SPIE, 1991, 1473(1):29-38.
[5] LI Yongkun, WANG Lei, FEI Yu. Periodic solution for shunting inhibitory cellular neural networks of neutral with time-varying delays in the leakage term on time scales[J]. Applied Mathematics, 2014, 2014(1):1-16.
[6] LI Yongkun, WANG Chao. Almost periodic solutions of shuntin inhibitory cellular neural networks on time scales[J]. Commun Nonlinear Sci Numer Simulat, 2012, 17(8):3258-3266.
[7] NGUÉRÉKATA G M. Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equation[J]. Semigroup Forum, 2004, 69(1):80-89.
[8] GOLDSTEIN J A, NGUÉRÉKATA G M. Almost automorphic solutions of semilinear evolution equations[J]. Proceedings of the American Mathematical Society, 2005, 133(8):2401-2408.
[9] EZZINBI K, FATAJOU S, NGUÉRÉKATA G M. A Cn-almost automorphic solutions for partial neutral functional differential equations[J]. Applicable Analysis, 2007, 86(9):1127-1146.
[10] HILGER S. Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten[D]. Würzburg: Universität Würzburg, 1988.
[11] BALASUBRAMANIAM P, NAGAMANI G, RAKKIYAPPAN R. Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(11):4422-4437.
[12] LI Xiaodi, CAO Jinde. Delay-dependent stability of neural networks of neutral type with time delay in the leakege term[J]. Nonlinearity, 2010, 23(7):1709-1726.
[13] BOHNER M, PETERSON A. Dynamic equations on time scales: an introduction with applications[M]. Boston: Birkhäuser, 2001.
[14] LI Yongkun, WANG Chao. Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales[J]. Abstract and Applied Analysis, 2011(Article ID 341520):1-22. DOI:10.1155/2011/341520.
[15] LI Yongkun, LI Yang.Almost automorphic solutin for neutral type high-order Hopfield neural networks with delays in leakage terms terms on time scales[J]. Applied Mathematics and Computation, 2014(1), 242:679-693.
[16] LIZAMA C, MESQUITA J G. Almost automorphic solutions of dynamic equations on time scales[J]. Journal of Functional Analysis, 2013, 265(10):2267-2311.
[17] LI Yongkun,WANG Huimei, MENG Xianfang. Almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks with time-varying and distributed delays[J]. IMA Journal of Mathematical Control and Information, 2018, 2018(00):1-31.
[18] XU Changjin, LI Peiluan. On anti-periodic solutions for neutral shunting inhibitory cellular neural networks with time-varying delays and D operator[J]. Neurocomputing, 2018, 275(1):377-382.
[19] XU Changjin, LI Peiluan. Periodic dynamics for memristor-based bidirectional associative memory neural networks with leakage delays and time-varying delays[J]. Control Automation and Systems, 2018, 16(2):535-549.
[20] LONG Zhiwen. New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms[J]. Neuro-computing, 2016, 171(1):503-509.
[1] 江静,高庆龄,张克玉. 时标上二阶Dirichlet边值问题弱解的存在性[J]. 山东大学学报(理学版), 2016, 51(6): 99-103.
[2] 范进军, 路晓东. 时标上带强迫项的二阶中立型时滞动力方程非振动解的存在性[J]. 山东大学学报(理学版), 2015, 50(05): 45-50.
[3] 赵娜. 时标上Sturm-Liouville问题的有限谱[J]. J4, 2013, 48(09): 96-102.
[4] 赵永昌1,王林山1,2. 具有不同时间尺度的分布时滞竞争神经网络概周期解的全局指数稳定性[J]. J4, 2010, 45(6): 60-64.
[5] 王顺康,王林山 . 具有马尔可夫跳跃参数的变时滞静态神经网络的全局指数稳定性[J]. J4, 2008, 43(4): 81-84 .
[6] 王 怡,刘爱莲 . 时标下的蛛网模型[J]. J4, 2007, 42(7): 41-44 .
[7] 张丽娟,斯力更 . 变时滞细胞神经网络的全局指数稳定性[J]. J4, 2007, 42(4): 58-62 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!