Generic and symmetric bifurcations analysis of a three dimensional economic model

J. Alidousti, Z. Eskandari and Z. Avazzadeh

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: This paper studies bifurcation analysis of an economic model by using the critical normal form coefficients method which is one of the most influential methods in bifurcation theory. This method advantageously checks the non-degeneracy condition without computing the central manifold and converting the linear part of the map into Jordan form. In this study, the codimension one and codimension two bifurcations of the model are investigated by considering different parameters and for each bifurcation, the normal form coefficients are computed. The obtained results conclude that the model undergoes bifurcations such as flip (period-doubling), Neimark-Sacker, resonance 1:3, resonance 1:4, Chenciner and period-doubling Neimark-Sacker. Furthermore, to accomplish symmetric bifurcation analysis of the model, the normal form of the Z3-symmetric double-1 multiplier bifurcation is utilized. The bifurcation curves of the model are drawn with the aid of the numerical continuation method. From the mathematical point of view, these bifurcation curves and numerical simulations not only support the theoretical results but also reveal more details of the dynamic system under study, especially after higher iterations. The achieved results directly can be applied to design and optimize many types of economic models.

Keywords: Bifurcation analysis; Neimark-Sacker; Fold; Period-doubling; Resonance; Chenciner (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077920306470
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306470

DOI: 10.1016/j.chaos.2020.110251

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().