具有非单调反馈的随机Mackey-Glass造血模型

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

具有非单调反馈的随机Mackey-Glass造血模型王文涛¹, 刘福窑¹, 陈娓²1. 上海工程技术大学数理与统计学院, 上海 201620;
2. 上海立信会计金融学院统计与数学学院, 上海 201209 Stochastic Mackey-Glass Model of Hematopoiesis with Non-monotone Feedback WANG Wentao¹, LIU Fuyao¹, CHEN Wei²1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China

摘要
图/表
参考文献
相关文章(8)
点击分布统计
下载分布统计
-->

全文: PDF(459 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要考虑到损坏率受到白噪声的干扰，本文介绍了一类具有非单调反馈的随机Mackey-Glass造血模型，用于描述其在随机环境中的动力学行为.首先，研究了在非负初值条件下全局正解的存在性和唯一性.接着，估计了解的平均最终有界性和Lyapunov指数.最后，给出了一个实例以及数值模拟以验证理论分析结果.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2018-09-20

PACS:

O193

基金资助:浙江省自然科学基金（LY18A010019）资助.

引用本文:

王文涛, 刘福窑, 陈娓. 具有非单调反馈的随机Mackey-Glass造血模型[J]. 应用数学学报, 2020, 43(5): 865-874. WANG Wentao, LIU Fuyao, CHEN Wei. Stochastic Mackey-Glass Model of Hematopoiesis with Non-monotone Feedback. Acta Mathematicae Applicatae Sinica, 2020, 43(5): 865-874.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2020/V43/I5/865

[1]	Mackey MC, Glass L. Oscillation and chaos in physiological control systems. Science, 1977, 197:287-289
[2]	Mackey MC. Mathematical models of hematopoietic cell replication and control. H.G. Othmer, F.R. Adler, M.A. Lewis, J.C. Dallon, eds. The Art of Mathematical Modelling:Case Studies in Ecology, Physiology and Biofluids, Prentice Hall, 1997, 149-178
[3]	Mackey M, Heiden U. Dynamic diseases and bifurcations in physiological control systems. Funk. Biol. Med., 1982, 1:156-164
[4]	Glass L, Mackey M. Mackey-Glass equation. Scholarpedia, 2010, 5(3):6908
[5]	Berezansky L, Braverman E. Mackey-Glass equation with variable coefficients. Comput. Math. Appl., 2006, 51:1-16
[6]	Berezansky L, Braverman E. On stability of some linear and nonlinear delay differential equations. J. Math. Anal. Appl., 2006, 314:391-411
[7]	Berezansky L, Braverman E. Stability and linearization for differential equations with a distributed delay. Funct. Differ. Equ., 2012, 19:27-43
[8]	Braverman E, Zhukovskiy S. Absolute and delay-dependent stability of equations with a distributed delay. Discrete Contin. Dyn. Syst. (A), 2012, 32:2041-2061
[9]	Jiang D, Wei J. Existence of positive periodic solutions for Volterra integro-differential equations. Acta Mathematica Scientia (B), 2001, 21(4):553-560
[10]	Wan A, Jiang D. Existence of positive periodic solutions for functional differential equations. Kyushu J. Math., 2002, 56:193-202
[11]	Wan A, Jiang D, Xu X. A new existence theory for positive periodic solutions to functional differential equations. Comput. Math. Appl., 2004, 47:1257-1262
[12]	翁佩萱, 梁妙莲. 一个造血模型周期解的存在性及其性态. 应用数学, 1995, 8(4):434-439(Weng P, Liang M. Existence and stability of periodic solution in a model of hematopoiesis. Math. Appl., 1995, 8(4):434-439)
[13]	Wang W. Global exponential stability for the Mackey-Glass model of respiratory dynamics with a control term. Math. Meth. Appl. Sci., 2016, 39:606-613
[14]	Wang X, Li Z. Erratum to:dynamics for a class of general hematopoiesis model with periodic coefficients. Appl. Math. Comput., 2008, 200(1):473-476
[15]	Weng P. Global attractivity of periodic solution in a model of hematopoiesis. Comput. Math. Appl., 2002, 44:1019-1030
[16]	Berezansky L, Braverman E, Idels L. Mackey-Glass model of hematopoiesis with non-monotone feedback:Stability, oscillation and control. Appl. Math. Comput., 2013, 219:6268-6283
[17]	May R M. Stability and complexity in model ecosystems. Princeton:Princeton University Press, 1973
[18]	Zhang J, Chen R, Nie L. Noise-enhanced stability in the time-delayed Mackey-Glass system. Indian J. Phys., 2015, 89:1321-1326
[19]	Nguyen D. Mackey-Glass equation driven by fractional Brownian motion. Physica A:Statistical Mechanics and its Applications, 2012, 391:5465-5472
[20]	Mao X. Stochastic differential equations and applications. Chichester:Horwood, 1997
[21]	Zhang J, Nie L, Yu L, Zhang X. Noise and time delay induce critical point in a bistable system. Int. J. Mod. Phys. (B), 2014, 28(28):1450197
[22]	Shu C, Nie L, Zhou Z. Stochastic resonance-like and resonance suppression-like phenomena in a bistable system with time delay and additive noise. Chinese Phys. Lett., 2012, 29(5):050506
[23]	Nie L, Mei D. Noise and time delay:Suppressed population explosion of the mutualism system. Europhys. Lett., 2007, 79:20005
[24]	Kloeden P E, Shardlow T. The Milstein scheme for stochastic delay differential equations without using anticipative calculus. Stoch. Anal. Appl., 2012, 30:181-202
[25]	Wang W, Wang L, Chen W. Stochastic Nicholson's blowflies delayed differential equations. Appl. Math. Lett., 2019, 87:20-26
[26]	Zhu Y, Wang K, Ren Y, Zhuang Y. Stochastic Nicholson's blowflies delay differential equation with regime switching. Appl. Math. Lett., 2019, 94:187-195
[27]	Yi X, Liu G. Analysis of stochastic Nicholson-type delay system with patch structure. Appl. Math. Lett., 2019, 96:223-229
[28]	Wang W, Shi C, Chen W. Stochastic Nicholson-type delay differential system. Int. J. Control, https://doi.org/10.1080/00207179.2019.1651941
[29]	Wang W, Chen W. Stochastic delay differential neoclassical growth model. Adv. Difference Equ., 2019, 2019:355

[1]	梁明杰, 王健. 可加Lévy噪声驱动随机微分方程的强Feller性与指数遍历性[J]. 应用数学学报, 2017, 40(2): 267-278.
[2]	周清, 李超. 分数Vasicek利率模型下几何平均亚式期权的定价公式[J]. 应用数学学报(英文版), 2014, 37(4): 662-675.
[3]	周少波. 马尔科夫切换型中立型随机泛函微分方程[J]. 应用数学学报(英文版), 2012, (6): 1128-1140.
[4]	肖艳清, 邹捷中. 分数布朗运动驱动下z一致连续的BSDE解的存在性与唯一性[J]. 应用数学学报(英文版), 2012, (2): 245-251.
[5]	黄可明. 高斯场最大值与最大模分布的某些收敛性[J]. 应用数学学报(英文版), 2000, 23(4): 625-631.
[6]	张书年. 关于有界性的勒茹米辛型定理[J]. 应用数学学报(英文版), 1999, 22(4): 497-503.
[7]	杨春鹏. 具有测度边值一类非线性方程解的存在性──概率处理[J]. 应用数学学报(英文版), 1999, 22(2): 215-221.
[8]	李森林, 黄立宏. 高维系统周期解的存在性与唯一性[J]. 应用数学学报(英文版), 1996, 19(1): 115-122.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14824