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.

scholarly journals Bifurcation and Chaotic Behavior of a Discrete-Time SIS Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Junhong Li ◽  
Ning Cui
Keyword(s):  
Hopf Bifurcation ◽  
Discrete Time ◽  
Chaotic Behavior ◽  
Euler Method ◽  
Flip Bifurcation ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Sis Model ◽  
Dynamical Behaviors ◽  
The Rich

The discrete-time epidemic model is investigated, which is obtained using the Euler method. It is verified that there exist some dynamical behaviors in this model, such as transcritical bifurcation, flip bifurcation, Hopf bifurcation, and chaos. The numerical simulations, including bifurcation diagrams and computation of Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors.

Study on Synchronization of the Centrifugal Flywheel Governor System

2013 ◽  
Vol 433-435 ◽  
pp. 21-29 ◽  
Author(s):  
Jian Kui Peng ◽  
Jian Ning Yu ◽  
Li Zhang ◽  
Ping Hu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Exponents ◽  
External Disturbance ◽  
Global Bifurcation ◽  
Control Methods ◽  
Chaotic Motions ◽  
Poincaré Sections ◽  
Dynamical Behaviors ◽  
System Synchronization ◽  
Poincare Sections

In this paper, the dynamical behaviors of the centrifugal flywheel governor with external disturbance is studied and it has abundant nonlinear behavior.The influence of system parameter is discussed by Lyapunov exponents spectrum and global bifurcation diagram, which accurately portray the partial dynamic behavior of the centrifugal flywheel governor. The routes to chaos are analyzed using Poincaré sections, which are found to be more complex . Periodic and chaotic motions can be clearly distinguished by Poincaré sections, bifurcation diagrams and Lyapunov exponents. Then, the paper proposes coupledfeedback control and adaptive control methods to achieve the chaotic the centrifugal flywheel governor system synchronization, the numerical simulation was provided in order to show the effectiveness of coupled feedback control and adaptive control methods for the synchronization of the chaotic nonautonomous centrifugal flywheel governor system.

scholarly journals Synchronization for a Class of Uncertain Fractional Order Chaotic Systems with Unknown Parameters Using a Robust Adaptive Sliding Mode Controller

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yan Yan
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Mode Synchronization ◽  
Robust Adaptive

This paper deals with the synchronization of a class of fractional order chaotic systems with unknown parameters and external disturbance. Based on the Lyapunov stability theory, a fractional order sliding mode is constructed and a controller is proposed to realize chaos synchronization. The presented method not only realizes the synchronization of the considered chaotic systems but also enhances the robustness of sliding mode synchronization. Finally, some simulation results demonstrate the effectiveness and robustness of the proposed method.

Dynamical Behaviors of a Modified Lorenz–Stenflo Chaotic System

2017 ◽  
Vol 27 (05) ◽  
pp. 1750074 ◽  
Author(s):  
Fuchen Zhang ◽  
Xingyuan Wang ◽  
Xiaofeng Liao ◽  
Guangyun Zhang ◽  
Chunlai Mu
Keyword(s):  
Chaos Synchronization ◽  
Chaos Control ◽  
Optimization Theory ◽  
Lyapunov Stability Theory ◽  
Theoretical Support ◽  
Dynamical Behaviors ◽  
Special Cases ◽  
Attractive Sets ◽  
Ultimate Bound ◽  
Theoretical Results

In this paper, the ultimate bound and globally exponentially attractive sets of a modified Lorenz–Stenflo system are studied based on the Lyapunov stability theory and optimization theory. Comparing with the best results in the current literature, our new results include the existing results as special cases. Furthermore, the new results offer a theoretical support to studying the Hausdorff dimension of attractor of this modified Lorenz–Stenflo system. These theoretical results are also important and useful for chaos control and chaos synchronization.

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

Turing Instability and Hopf Bifurcation in Cellular Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150143
Author(s):  
Zunxian Li ◽  
Chengyi Xia
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Turing Instability ◽  
Cellular Neural Networks ◽  
Bifurcation Theorem ◽  
Decoupling Method ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Approximate Expressions ◽  
Zero Equilibrium

In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and Hopf bifurcation at the zero equilibrium are derived. Furthermore, the approximate expressions of the bifurcating periodic solutions are also obtained by using the Hopf bifurcation theorem. Finally, numerical simulations are provided to demonstrate the theoretical results.

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
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