Dynamics in a Van Der Pol Model with Delay

被引：0

作者：

Xu Changjin ^{[1
]}

Li Peiluan ^{[2
]}

Yao Lingyun ^{[3
]}

机构：

[1] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China

[2] Henan Univ Sci & Technol, Dept Math & Stat, Luoyang 471003, Peoples R China

[3] Univ Finance & Econ, Guiyang 550004, Peoples R China

来源：

PROGRESS IN INDUSTRIAL AND CIVIL ENGINEERING, PTS. 1-5 | 2012年 / 204-208卷

基金：

中国国家自然科学基金;

关键词：

Van Der Pol model; Delay; Stability; Hopf bifurcation; BIFURCATION; OSCILLATOR;

D O I：

10.4028/www.scientific.net/AMM.204-208.4586

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, the dynamics of a van der pol model with delay are considered. It is shown that the asymptotic behavior depends crucially on the time delay parameter. By regarded the delay as a bifurcation parameter, we are particularly interested in the study of the Hopf bifurcation problem. The length of delay which preserves the stability of the equilibrium is calculated. Some numerical simulations for justifying the analytical findings are included.

引用

页码：4586 / +

页数：2

共 6 条

[1] Hopf bifurcation in a van der Pol type oscillator with magnetic hysteresis
Appelbe, B.
Rachinskii, D.
Zhezherun, A.
[J]. PHYSICA B-CONDENSED MATTER, 2008, 403 (2-3) : 301 - 304
[2] Fofana M.S., 2005, Int. J. Math. and Mathematical Science, V2, P311
[3] THE TRADE-OFF BETWEEN MUTUAL INTERFERENCE AND TIME LAGS IN PREDATOR PREY SYSTEMS
FREEDMAN, HI
RAO, VSH
[J]. BULLETIN OF MATHEMATICAL BIOLOGY, 1983, 45 (06) : 991 - 1004
[4] Hale J.K., 1977, THEORY FUNCTIONAL DI
[5] Kuang Y., 1993, Delay Differential Equations with Applications in Population Dynamics
[6] Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback
Wang, Hongbin
Jiang, Weihua
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 368 (01) : 9 - 18

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