Hopf bifurcation control for affine systems

2004 ◽  
Author(s):  
F. Verduzco ◽  
J. Alvarez
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Control ◽  
Affine Systems

scholarly journals Hopf Bifurcation Control in a Lorenz Type System

2018 ◽  
Vol 06 (08) ◽  
pp. 1704-1719
Author(s):  
P. E. Calderon-Saavedra ◽  
E. Munoz-Aguirre ◽  
J. Alvarez-Mena ◽  
S. Gomez-Perez
Keyword(s):  
Hopf Bifurcation ◽  
Type System ◽  
Bifurcation Control

Hopf bifurcation control of congestion control model in a wireless access network

2014 ◽  
Vol 144 ◽  
pp. 159-168 ◽  
Author(s):  
Dawei Ding ◽  
Xuemei Qin ◽  
Tingting Wu ◽  
Nian Wang ◽  
Dong Liang
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
Access Network ◽  
Control Model ◽  
Bifurcation Control ◽  
Wireless Access ◽  
Wireless Access Network

scholarly journals Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dawei Ding ◽  
Chun Wang ◽  
Lianghui Ding ◽  
Nian Wang ◽  
Dong Liang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Feedback Control ◽  
Congestion Control ◽  
State Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Fast Tcp ◽  
Hybrid Controller ◽  
Control Schemes

We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model.

BIFURCATION CONTROL OF A CONGESTION CONTROL MODEL VIA STATE FEEDBACK

2013 ◽  
Vol 23 (06) ◽  
pp. 1330018 ◽  
Author(s):  
MIN XIAO ◽  
WEI XING ZHENG ◽  
JINDE CAO
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
State Feedback ◽  
Stability Domain ◽  
Control Model ◽  
The State ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Gain Parameter ◽  
State Feedback Controller

This paper proposes to use a state feedback method to control the Hopf bifurcation for a novel congestion control model, i.e. the exponential random early detection (RED) algorithm with a single link and a single source. The gain parameter of the congestion control model is chosen as the bifurcation parameter. The analysis shows that in the absence of the state feedback controller, the model loses stability via the Hopf bifurcation early, and can maintain a stationary sending rate only in a certain domain of the gain parameter. When applying the state feedback controller to the model, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the model possesses a stable sending rate in a larger parameter range. Furthermore, explicit formulae to determine the properties of the Hopf bifurcation are obtained. Numerical simulations are given to justify the validity of the state feedback controller in bifurcation control.

scholarly journals Bifurcation Control of a Delayed Fractional Mosaic Disease Model for Jatropha curcas with Farming Awareness

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Shouzong Liu ◽  
Mingzhan Huang ◽  
Juan Wang
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Jatropha Curcas ◽  
Mosaic Disease ◽  
Bifurcation Control ◽  
Feedback Gain ◽  
Infection Model ◽  
Feedback Delay ◽  
Execution Delay ◽  
Farming Awareness

In this paper, the bifurcation control of a fractional-order mosaic virus infection model for Jatropha curcas with farming awareness and an execution delay is investigated. By analyzing the associated characteristic equation, Hopf bifurcation induced by the execution delay is studied for the uncontrolled system. Then, a time-delayed controller is introduced to control the occurrence of Hopf bifurcation. Our study implies that bifurcation dynamics is significantly affected by the change of the fractional order, the feedback gain and the extended feedback delay provided that the other parameters are fixed. A series of numerical simulations is performed, which not only verifies our theoretical results but also reveals some specific features. Numerically, we find that the Hopf bifurcation gradually occurs in advance with the increase of the fractional order, and there exist extreme points for the feedback gain and the extended feedback delay which can minimize the bifurcation value.

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