scholarly journals A Continuous Time Bertrand Duopoly Game With Fractional Delay and Conformable Derivative: Modeling, Discretization Process, Hopf Bifurcation, and Chaos

2019 ◽  
Vol 7 ◽  
Author(s):  
Baogui Xin ◽  
Wei Peng ◽  
Luca Guerrini
Keyword(s):  
Hopf Bifurcation ◽  
Continuous Time ◽  
Conformable Derivative ◽  
Bifurcation And Chaos ◽  
Fractional Delay ◽  
Discretization Process

Hopf bifurcation and chaos in macroeconomic models with policy lag

2005 ◽  
Vol 25 (1) ◽  
pp. 91-108 ◽  
Author(s):  
Xiaofeng Liao ◽  
Chuandong Li ◽  
Shangbo Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation And Chaos ◽  
Macroeconomic Models

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

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