Hopf bifurcation analysis in a modified price differential equation model with two delays
type: Item
instance of: scholarly article
title: Hopf bifurcation analysis in a modified price differential equation model with two delays
zbMATH Open document ID: 1474.91098
DOI: 10.1155/2014/686274
author: Ying Xiong
author: Xiaona Ma
author: Yanhui Zhai
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid.
Mathematics Subject Classification ID: 91B55
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 7022879
Wikidata QID: Q59040601
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/686274
OpenAlex ID: W1989449907
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description: scientific article; zbMATH DE number 7022879