Discretizing dynamical systems with generalized Hopf bifurcations

被引：1
|
作者：
Paez Chavez, Joseph [1 ]
机构：
[1] Escuela Super Politecn Litoral, Inst Ciencias Matemat, Guayaquil, Ecuador
来源：
NUMERISCHE MATHEMATIK | 2011年 / 118卷 / 02期
关键词：
DIFFERENTIAL-EQUATION; SACKER BIFURCATIONS; TAKENS-BOGDANOV; POINTS; COMPUTATION; ODES;
D O I：
10.1007/s00211-010-0340-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the discretizations of parameter-dependent, continuous-time dynamical systems. We show that the general one-step methods shift a generalized Hopf bifurcation and turn it into a generalized Neimark-Sacker point. We analyze the effect of discretization methods on the emanating Hopf curve. In particular, we obtain estimates for the eigenvalues of the discretized system along this curve. A detailed analysis of the discretized first Lyapunov coefficient is also given. The results are illustrated by a numerical example. Dynamical consequences are discussed.
引用
收藏
页码：229 / 246
页数：18
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