Journal of Guangxi Normal University(Natural Science Edition) ›› 2019, Vol. 37 ›› Issue (3): 106-110.doi: 10.16088/j.issn.1001-6600.2019.03.012

Previous Articles     Next Articles

Random Dynamics for Stochastic Delay Lattice Systems in Xρ Space

ZHANG Yijin1,2   

  1. 1.Chongqing Key Lab of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
    2.Key Laboratory of Industrial Internetof Things and Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications,Chongqing 400065, China
  • Online:2019-07-12 Published:2019-07-12

PDF (PC)

408

Abstract: The dynamics of a class of stochastic lattice dynamical systems with time delay driven by additive white noise is studied. Xρ space is introduced, basic equalities, Young inequality, Gronwall inequality and Schwarz inequality are applied. The existence, uniqueness and continuous dependence on the initial data of solutions to the stochastic delay lattice equations with additive noise are presented. Then a continuous infinite dimensional random dynamical system generated by the solutions is obtained.

Key words: random dynamical system, delay equation, lattice systems, continuous dependence, dynamics

CLC Number: 

  • O175.2
[1] BELL J, COSNER C. Threshold behaviour and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons [J]. Quarterly of Applied Mathematics, 1984,42:1-14.
[2] CHUA L O, ROSKA T. The CNN paradigm [J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1993,40:147-156.
[3] KEENER J P. The effects of discrete gap junction coupling on propagation in myocardium [J]. Journal of Theoretical Biology, 1991,148:49-82.
[4] ERNEUX T, NICOLIS G. Propagating waves in discrete bistable reaction diffusion systems[J]. Physica D,1993,67:237-244.
[5] BATES P W, LISEI H, LU K N. Attractors for stochastic lattice dynamical systems[J]. Stochastics and Dynamics, 2006,6:1-21.
[6] HALE J K, VERDUYN LUNEL S M. Introduction to functional differential equations[M]. New York: Springer-Verlag,1993.
[7] MOHAMMED S E A. Stochastic functional differential equations[M]. Boston: Pitman Advanced Publishing Program,1984.
[8] WU J. Theory and applications of partial functional differential equations[M]. New York: Springer-Verlag, 1996.
[9] ARNOLD L. Random dynamical systems[M]. Berlin:Springer-Verlag,1998.
[10]ZHAO W, ZHANG Y. Compactness and attracting of random attractors for non-autonomous stochastic lattice dynamical systems in weighted space, pρ [J]. Applied Mathematics & Computation, 2016, 291:226-243.
[1] SHE Lianbing, GAO Yunlong. Backward-compact Dynamics for Non-autonomous Navier-Stokes Equations on Unbounded Domains [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(1): 41-46.
[2] HONG Lingling, YANG Qigui. Research on Complex Dynamics of a New 4D Hyperchaotic System [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(3): 96-105.
[3] WANG Yi, ZOU Yanli, LI Ke, HUANG Li. The Influence of the Distributed Power Station Connection Modeson the Power Grid Synchronization [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(4): 24-31.
[4] LIU Huimin, GUAN Dongjie, ZHANG Mengjie. Stress Factorsand Stress Mechanism on Subsequent Developmentof Ecological Security in the Three Gorges Reservoir Area [J]. Journal of Guangxi Normal University(Natural Science Edition), 2016, 34(3): 150-158.
[5] QIN Jian, CHEN Shan-zhen, BAI Ke-zhao, KONG Ling-jiang. Subconscious Effect on Pedestrian Emergency Evacuation [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(3): 27-32.
[6] LIAO Zhi-xian, LUO Xiao-shu, HUANG Guo-xian. Non-linear Dynamics Model and Chaotic Behavior of the Single-phase Full Bridge Photovoltaic Grid-connected Inverter [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(4): 1-6.
[7] XIE Guang-qiang, ZHANG Yun, LI Yang, ZENG Qi-jie. Research of Krause's Multi-Agent Consensus Model [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(3): 106-113.
[8] GAO Jun-fen, HU Wei-ping. Recognition and Study of Pathological Voices Based on NonlinearDynamics Using GMM [J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(3): 5-8.
[9] XIONG Fei-bing, YANG Feng. Fluorescence Decay Dynamics of Praseodymium Ions Doped in Lead Tungstate Crystal [J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(2): 71-75.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] MENG Chunmei, LU Shiyin, LIANG Yonghong, MO Xiaomin, LI Weidong, HUANG Yuanjie, CHENG Xiaojing, SU Zhiheng, ZHENG Hua. Electron Microscopy Study on the Apoptosis and Autophagy of the Hepatic Stellate Cells Induced by Total Alkaloids[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 76 -79 .
[2] LI Yuhui, CHEN Zening, HUANG Zhonghao, ZHOU Qihai. Activity Time Budget of Assamese macaque (Macaca assamensis) during Rainy Season in Nonggang Nature Reserve, Guangxi, China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 80 -86 .
[3] QIN Yingying, QI Guangchao, LIANG Shichu. Effects of Eichhornia crassipes Aqueous Extracts on Seed Germination of Ottelia acuminata var. jingxiensis[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 87 -92 .
[4] WEI Hongjin, ZHOU Xile, JIN Dongmei, YAN Yuehong. Additions to the Pteridophyte Flora of Hunan, China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 101 -106 .
[5] BAO Jinping, ZHENG Lianbin, YU Keli, SONG Xue, TIAN Jinyuan, DONG Wenjing. Skinfold Thickness Characteristics of Yi Adults in Daliangshan,China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 107 -112 .
[6] LIN Yongsheng, PEI Jianguo, ZOU Shengzhang, DU Yuchao, LU Li. Red Bed Karst and Its Hydrochemical Characteristics of Groundwater in the Downstream of Qingjiang River, China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 113 -120 .
[7] ZHANG Ru, ZHANG Bei, REN Hongrui. Spatio-temporal Dynamics Analysis and Its Affecting Factors of Cropland Loss in Xuangang Mining Area, Shanxi, China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 121 -132 .
[8] LI Xianjiang, SHI Shuqin, CAI Weimin, CAO Yuqing. Simulation of Land Use Change in Tianjin Binhai New Area Based on CA-Markov Model[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 133 -143 .
[9] WANG Mengfei, HUANG Song. Spatial Linkage of Tourism Economy of Cities in West River Economic Belt in Guangxi, China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 144 -150 .
[10] TENG Zhijun, LÜ Jinling, GUO Liwen, XU Yuanyuan. Coverage Strategy of Wireless Sensor Network Based on Improved Particle Swarm Optimization Algorithm[J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 9 -16 .
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd