Discretizing dynamical systems with Hopf-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：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2012年 / 32卷 / 01期

关键词：

bifurcation problems; ordinary differential equations; one-step methods; COMPUTATION; EQUATIONS; POINTS;

D O I：

10.1093/imanum/drr002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the discretization of two-parameter, continuous-time dynamical systems. We prove that one-step methods turn Hopf-Hopf bifurcations into double Neimark-Sacker points. We discuss the effect of the discretization methods on the bifurcation diagram. The numerical approximation of the critical eigenvalues is analysed. The results are illustrated by a numerical example.

引用

页码：185 / 201

页数：17

共 50 条

[1] Discretizing dynamical systems with generalized Hopf bifurcations
Joseph Páez Chávez
[J]. Numerische Mathematik, 2011, 118 : 229 - 246
[2] Discretizing dynamical systems with generalized Hopf bifurcations
Paez Chavez, Joseph
[J]. NUMERISCHE MATHEMATIK, 2011, 118 (02) : 229 - 246
[3] Hopf bifurcations in dynamical systems
Rionero, Salvatore
[J]. RICERCHE DI MATEMATICA, 2019, 68 (02) : 811 - 840
[4] Hopf bifurcations in dynamical systems
Salvatore Rionero
[J]. Ricerche di Matematica, 2019, 68 : 811 - 840
[5] On some secondary bifurcations near resonant Hopf-Hopf interactions
LeBlanc, VG
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS, 2000, 7 (03): : 405 - 427
[6] Ionization waves: Hopf-Hopf bifurcations and nonlinear wave-wave interactions
Bruhn, B
[J]. PHYSICS OF PLASMAS, 2004, 11 (09) : 4446 - 4455
[7] A DYNAMICAL SYSTEM WITH HOPF BIFURCATIONS AND CATASTROPHES
MURATORI, S
RINALDI, S
[J]. APPLIED MATHEMATICS AND COMPUTATION, 1989, 29 (01) : 1 - 15
[8] Hopf-Hopf interactions of surge and rotating stall
Coller, B. D.
[J]. JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2006, 1 (04): : 320 - 327
[9] HOPF BIFURCATIONS IN DYNAMICAL SYSTEMS VIA ALGEBRAIC TOPOLOGICAL METHOD
Jawarneh, Ibrahim
Altawallbeh, Zuhier
[J]. MATEMATICKI VESNIK, 2023, 75 (03): : 216 - 224
[10] Resonant hopf-hopf interactions in delay differential equations
Campbell S.A.
LeBlanc V.G.
[J]. Journal of Dynamics and Differential Equations, 1998, 10 (2) : 327 - 346

← 1 2 3 4 5 →