Hopf Bifurcation Control for a Single Neuron Model with Delay-Dependent Parameters via State Feedback

2011 ◽  
pp. 132-138
Author(s):  
Min Xiao
Keyword(s):  
Hopf Bifurcation ◽  
State Feedback ◽  
Single Neuron ◽  
Neuron Model ◽  
Bifurcation Control ◽  
Delay Dependent

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 Controlling hopf bifurcations: Discrete-time systems

2000 ◽  
Vol 5 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Guanrong Chen ◽  
Jin-quing Fang ◽  
Yiguang Hong ◽  
Huashu Qin
Keyword(s):  
Hopf Bifurcation ◽  
Computer Simulations ◽  
Discrete Time ◽  
State Feedback ◽  
Bifurcation Control ◽  
Hopf Bifurcations ◽  
Control Task ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Theoretical Results

Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback methodology is developed in this paper for Hopf bifurcation control for discrete-time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.

Stability and Hopf Bifurcation Analysis in Hindmarsh–Rose Neuron Model with Multiple Time Delays

2016 ◽  
Vol 26 (11) ◽  
pp. 1650187 ◽  
Author(s):  
Dongpo Hu ◽  
Hongjun Cao
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Time Delays ◽  
Single Neuron ◽  
Neuron Model ◽  
Multiple Time ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Multiple Time Delays ◽  
The Stability

In this paper, the dynamical behaviors of a single Hindmarsh–Rose neuron model with multiple time delays are investigated. By linearizing the system at equilibria and analyzing the associated characteristic equation, the conditions for local stability and the existence of local Hopf bifurcation are obtained. To discuss the properties of Hopf bifurcation, we derive explicit formulas to determine the direction of Hopf bifurcation and the stability of bifurcated periodic solutions occurring through Hopf bifurcation. The qualitative analyses have demonstrated that the values of multiple time delays can affect the stability of equilibrium and play an important role in determining the properties of Hopf bifurcation. Some numerical simulations are given for confirming the qualitative results. Numerical simulations on the effect of delays show that the delays have different scales when the two delay values are not equal. The physiological basis is most likely that Hindmarsh–Rose neuron model has two different time scales. Finally, the bifurcation diagrams of inter-spike intervals of the single Hindmarsh–Rose neuron model are presented. These bifurcation diagrams show the existence of complex bifurcation structures and further indicate that the multiple time delays are very important parameters in determining the dynamical behaviors of the single neuron. Therefore, these results in this paper could be helpful for further understanding the role of multiple time delays in the information transmission and processing of a single neuron.

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