Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps

Reza Mazrooei-Sebdani, Zohreh Eskandari, Hil Gaétan Ellart Meijer

Research output: Book/ReportReportOther research output

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Abstract

We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages14
Publication statusPublished - Feb 2017

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.2058
ISSN (Print)1874-4850

Keywords

  • EWI-27788
  • IR-104021

Cite this

Mazrooei-Sebdani, R., Eskandari, Z., & Meijer, H. G. E. (2017). Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. (Memorandum / Department of Applied Mathematics; No. 2058). Enschede: University of Twente, Department of Applied Mathematics.
Mazrooei-Sebdani, Reza ; Eskandari, Zohreh ; Meijer, Hil Gaétan Ellart. / Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. Enschede : University of Twente, Department of Applied Mathematics, 2017. 14 p. (Memorandum / Department of Applied Mathematics; 2058).
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Mazrooei-Sebdani, R, Eskandari, Z & Meijer, HGE 2017, Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. Memorandum / Department of Applied Mathematics, no. 2058, University of Twente, Department of Applied Mathematics, Enschede.

Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. / Mazrooei-Sebdani, Reza; Eskandari, Zohreh; Meijer, Hil Gaétan Ellart.

Enschede : University of Twente, Department of Applied Mathematics, 2017. 14 p. (Memorandum / Department of Applied Mathematics; No. 2058).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps

AU - Mazrooei-Sebdani, Reza

AU - Eskandari, Zohreh

AU - Meijer, Hil Gaétan Ellart

PY - 2017/2

Y1 - 2017/2

N2 - We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.

AB - We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.

KW - EWI-27788

KW - IR-104021

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Mazrooei-Sebdani R, Eskandari Z, Meijer HGE. Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. Enschede: University of Twente, Department of Applied Mathematics, 2017. 14 p. (Memorandum / Department of Applied Mathematics; 2058).