Abstract and Applied Analysis

Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays

Yanhui Zhai, Ying Xiong, and Xiaona Ma

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 686274, 8 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607559

Digital Object Identifier
doi:10.1155/2014/686274

Mathematical Reviews number (MathSciNet)
MR3178883

Zentralblatt MATH identifier
07022879

Citation

Zhai, Yanhui; Xiong, Ying; Ma, Xiaona. Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 686274, 8 pages. doi:10.1155/2014/686274. https://projecteuclid.org/euclid.aaa/1412607559


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