Stability and Local Hopf Bifurcation Analysis in Rayleigh Price Model with Two Time Delays

2018 ◽  
Vol 60 (2) ◽  
pp. 60-69
Author(s):  
Lei Peng ◽  
◽  
Yanhui Zhai
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Time Delays ◽  
Price Model ◽  
Local Hopf Bifurcation

Hopf bifurcation analysis of a tumor virotherapy model with two time delays

2020 ◽  
Vol 553 ◽  
pp. 124266 ◽  
Author(s):  
Hui-zhong Li ◽  
Xiang-dong Liu ◽  
Rui Yan ◽  
Cheng Liu
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Time Delays

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

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yanhui Zhai ◽  
Ying Xiong ◽  
Xiaona Ma
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Quadratic Function ◽  
Equation Model ◽  
Price Model ◽  
Differential Equation Model ◽  
Normal Form Theory ◽  
Price Differential ◽  
Local Hopf Bifurcation ◽  
Two Delays

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.

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