Bifurcation analysis in a scalar delay differential equation
作者： Junjie Wei
DOI: 10.1088/0951-7715/20/11/002
关键词:
摘要: The dynamics of a scalar delay differential equation, which includes Mackey–Glass equations, are investigated. We prove that sequence Hopf bifurcations occurs at the equilibrium as increases. An explicit algorithm for determining direction and stability bifurcating periodic solutions is derived, using theory normal form centre manifold. global existence multiple established bifurcation result given by Wu (1998 Trans. Am. Math. Soc. 350 4799) Bendixson criterion higher dimensional ordinary equations Li Muldowney (1993 J. Diff. Eqns 106 27).
harvard.edu
sci-hub.se 参考文章(63)
Jack K. Hale, Theory of Functional Differential Equations ,(1977)
Alexander L. Skubachevskii, Hans-Otto Walther, On the Floquet Multipliers of Periodic Solutions to Non-linear Functional Differential Equations Journal of Dynamics and Differential Equations. ,vol. 18, pp. 257- 355 ,(2006) , 10.1007/S10884-006-9006-5
Y. Li, J.S. Muldowney, On Bendixson′s Criterion Journal of Differential Equations. ,vol. 106, pp. 27- 39 ,(1993) , 10.1006/JDEQ.1993.1097
Junjie Wei, Yuan Yuan, Synchronized Hopf bifurcation analysis in a neural network model with delays Journal of Mathematical Analysis and Applications. ,vol. 312, pp. 205- 229 ,(2005) , 10.1016/J.JMAA.2005.03.049
M. Mackey, L Glass, Oscillation and chaos in physiological control systems Science. ,vol. 197, pp. 287- 289 ,(1977) , 10.1126/SCIENCE.267326
JUNJIE WEI, DEJUN FAN, Hopf Bifurcation Analysis in a MACKEY-GLASS System International Journal of Bifurcation and Chaos. ,vol. 17, pp. 2149- 2157 ,(2007) , 10.1142/S0218127407018282
GUANRONG CHEN, JORGE L. MOIOLA, HUA O. WANG, BIFURCATION CONTROL: THEORIES, METHODS, AND APPLICATIONS International Journal of Bifurcation and Chaos. ,vol. 10, pp. 511- 548 ,(2000) , 10.1142/S0218127400000360
Junjie Wei, Michael Y. Li, Hopf bifurcation analysis in a delayed Nicholson blowflies equation Nonlinear Analysis-theory Methods & Applications. ,vol. 60, pp. 1351- 1367 ,(2005) , 10.1016/J.NA.2003.04.002
Leon Glass, Michael C. Mackey, PATHOLOGICAL CONDITIONS RESULTING FROM INSTABILITIES IN PHYSIOLOGICAL CONTROL SYSTEMS* Annals of the New York Academy of Sciences. ,vol. 316, pp. 214- 235 ,(1979) , 10.1111/J.1749-6632.1979.TB29471.X
Junjie Wei, Xingfu Zou, Bifurcation analysis of a population model and the resulting SIS epidemic model with delay Journal of Computational and Applied Mathematics. ,vol. 197, pp. 169- 187 ,(2006) , 10.1016/J.CAM.2005.10.037