Hopf Bifurcation and Chaos Synchronization for a Class of Mechanical Centrifugal Flywheel Governor System

2007 ◽  
pp. 349-352
Author(s):  
Yan Dong Chu ◽  
Jian Gang Zhang ◽  
Xian Feng Li ◽  
Ying Xiang Chang
Keyword(s):  
Hopf Bifurcation ◽  
Chaos Synchronization ◽  
Bifurcation And Chaos

Studying on the Synchronization of a Mechanical Centrifugal Flywheel Governor System

2008 ◽  
Vol 385-387 ◽  
pp. 309-312
Author(s):  
Yan Dong Chu ◽  
Jian Gang Zhang ◽  
Xian Feng Li ◽  
Ying Xiang Chang
Keyword(s):  
Hopf Bifurcation ◽  
Chaos Synchronization ◽  
System Parameter ◽  
External Disturbance ◽  
Global Bifurcation ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Bifurcation And Chaos ◽  
Proper System ◽  
Dynamical Behaviors

In this paper, the dynamical behaviors of the centrifugal flywheel governor with external disturbance are discussed, and the system exhibits exceedingly complicated dynamic behaviors. The influence of system parameter on the chaotic system is discussed through Lyapunov-exponents spectrum and global bifurcation diagram, which accurately portray the partial dynamic behavior of the system. It is chaotic with proper system parameter, and we utilize Poincaré sections to study the Hopf bifurcation and chaos forming of the centrifugal flywheel governor system. Then, we utilize coupled-feedback control and adaptive control to realize the chaotic synchronization and obtain the conditions of chaos synchronization. Finally, we carry on the theory proof using the Lyapunov stability theory to the obtained conditions, the theoretical proof and number simulation shows the effectiveness of these methods.

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.

Sign in / Sign up

Export Citation Format

Share Document