Biological delay systems and the Mikhailov criterion of stability

被引：37
|
作者：
Forys, U [1 ]
机构：
[1] Warsaw Univ, Fac Math Informat & Mech, Inst Appl Math & Mech, PL-02097 Warsaw, Poland
来源：
JOURNAL OF BIOLOGICAL SYSTEMS | 2004年 / 12卷 / 01期
关键词：
delay differential equation; characteristic quasi-polynomial; stability; Lapunov stability; Hopf bifurcation;
D O I：
10.1142/S0218339004001014
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
This paper deals with the stability analysis of biological delay systems. The Mikhailov criterion of stability is presented (and proved in the Appendix) for the case of discrete delay and distributed delay (i.e., delay in integral form). This criterion is used to check stability regions for some well-known equations, especially for the delay logistic equation and other equations with one discrete delay which appear in many applications. Some illustrations of the behavior of Mikhailov hodograph are shown.
引用
收藏
页码：45 / 60
页数：16
相关论文
共 50 条
  • [21] A New Criterion for Stability of Large-Scale Systems with Delay
    周少武
    JournalofSystemsEngineeringandElectronics, 2001, (04) : 59 - 65
  • [22] FREQUENCY CRITERION OF STABILITY OF VARIABLE-STRUCTURE SYSTEMS WITH DELAY
    ABDULLAEV, AA
    DZHAFAROV, EM
    AUTOMATION AND REMOTE CONTROL, 1979, 40 (06) : 939 - 944
  • [23] Stability Analysis of Neutral Systems: A Delay-Dependent Criterion
    Ionescu, Tudor C.
    Stefan, Radu
    TOPICS IN TIME DELAY SYSTEMS: ANALYSIS, ALGORITHMS AND CONTROL, 2009, 388 : 15 - +
  • [24] SIMPLE STABILITY CRITERION FOR A CLASS OF DELAY DIFFERENTIAL SYSTEMS.
    Buslowicz, M.
    1600, (18):
  • [25] Novel stability criterion of time delay systems with nonlinear uncertainties
    Park, JH
    Kwon, O
    APPLIED MATHEMATICS LETTERS, 2005, 18 (06) : 683 - 688
  • [26] SOME GENERALIZATIONS OF MIKHAILOV CRITERION
    PETRIC, JJ
    AUTOMATION AND REMOTE CONTROL, 1965, 26 (12) : 2031 - &
  • [27] Modified Mikhailov stability criterion for non-commensurate fractional-order neutral differential systems with delays
    Thai, Ha Duc
    Tuan, Hoang The
    JOURNAL OF THE FRANKLIN INSTITUTE, 2025, 362 (01)
  • [28] A new delay-dependent stability criterion for singular time-delay systems
    Gao, Huanli
    Xu, Bugong
    Zhang, Yougang
    Hou, Xiaoli
    2007 IEEE INTERNATIONAL CONFERENCE ON CONTROL AND AUTOMATION, VOLS 1-7, 2007, : 360 - 364
  • [29] A new robust delay-dependent stability criterion for a class of uncertain systems with delay
    Hao, F
    Wang, L
    Chu, TG
    PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, : 5433 - 5437
  • [30] A Delay-dependent Stability Criterion for A Class of Systems With Time-varying Delay
    Jiang, Xiefu
    Yang, Shuai
    PROCEEDINGS OF THE 28TH CHINESE CONTROL AND DECISION CONFERENCE (2016 CCDC), 2016, : 2296 - 2299
12345