[1]曾晓云,侯成敏*,胡正高.一类带脉冲呼吸系统疾病模型的周期解的存在性[J].延边大学学报(自然科学版),2015,41(01):5-9.
　ZENG Xiaoyun,HOU Chengmin*,HU Zhenggao.Existence of periodic solutions for a respiratory diseases model with impulse[J].Journal of Yanbian University,2015,41(01):5-9.
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一类带脉冲呼吸系统疾病模型的周期解的存在性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第41卷 期数: 2015年01期 页码: 5-9 栏目: 基础科学研究 出版日期: 2015-03-20
Title:
Existence of periodic solutions for a respiratory diseases model with impulse
作者:
曾晓云1;  侯成敏2*;  胡正高3
1.海军航空工程学院 系统科学与数学研究所, 山东 烟台 264001; 2.延边大学理学院 数学系, 吉林 延吉 133002; 3.海军航空工程学院 控制工程系, 山东 烟台 264001
Author(s):
ZENG Xiaoyun1;  HOU Chengmin2*;  HU Zhenggao3
1.Institute of Systems Science and Mathematic, Naval Aeronautical and Astronautical University, Yantai 264001, China; 2.Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China; 3.Department of Control Engineering, Naval Aeronautics and Astronautics University, Yantai 264001, China
关键词:
脉冲;  正周期解;  迭合度;  呼吸系统
Keywords:
impulse;  positive periodic solution;  coincidence degree;  respiratory dynamics
分类号:
O175.13
文献标志码:
A
摘要:
研究了具有脉冲效应的呼吸系统疾病模型,首先运用不等式技巧给出了该系统解的先验上界估计,其次运用迭合度理论中的延拓定理,得到了该系统至少存在一个正周期解的充分条件.
Abstract:
A respiratory diseases model with impulsive effects is investigated in this paper. A prior upper bound estimation for the solution of the system is given firstly. Using Gaines and Mawhin’s continuation theorem from coincidence degree theory, we obtain the sufficient condition which ensures the system have at least one positive periodic solution.

参考文献/References:

[1] Mackey M C, Glass L. Oscillation and chaos in physiological control system[J]. Science, 1977,197:287-289.
[2] Saker S H, Agarwal S. Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics[J]. Comput Math Appl, 2002,44(5/6):623-632.
[3] Chen Y, Huang L. Existence and global attractivity of a positive periodic solution of a delayed periodic respiration model[J]. Computers and Mathematics with Applications, 2005,49(5):677-687.
[4] Bainov D, Simeonov P. Impulsive Differential Equations: Periodic Solutions and Applications[M]. Harlow: Longman Scientific & Technical, 1993.
[5] Sun T, Xi H. Global attractivity for a family of nonlinear difference equations[J]. Appl Math Lett, 2007,20(7):741-745.
[6] Wang W T. Positive pseudo almost periodic solutions for a class of differential iterative equations with biological background[J]. Appl Math Lett, 2015,46:106-110.
[7] Zhang H, Wang L, Yang M. Existence and exponential convergence of the positive almost periodic solution for a model of hematopoiesi[J]. Appl Math Lett, 2013,26:38-42.

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备注/Memo

收稿日期: 2014-12-11 基金项目: 国家自然科学基金资助项目(11161049)*通信作者: 侯成敏(1963—),女,教授,研究方向为微分方程理论及其应用.

更新日期/Last Update: 2015-03-20