scholarly journals Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller

2016 ◽  
Vol 26 (11) ◽  
pp. 113120 ◽  
Author(s):  
Huan Su ◽  
Xuerong Mao ◽  
Wenxue Li
Keyword(s):  
Hopf Bifurcation ◽  
Discrete Time ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Differential Systems ◽  
Delayed Feedback Controller ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Time Delayed Feedback

HOPF BIFURCATION CONTROL FOR AN INTERNET CONGESTION MODEL

2005 ◽  
Vol 15 (08) ◽  
pp. 2643-2651 ◽  
Author(s):  
Z. CHEN ◽  
P. YU
Keyword(s):  
Hopf Bifurcation ◽  
Polynomial Function ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Higher Dimensional ◽  
Positive Gain ◽  
Delayed Feedback Controller ◽  
Internet Congestion ◽  
Delay Differential ◽  
Time Delayed Feedback

In this note, we consider Hopf bifurcation control for an Internet congestion model with a single route accessed by a single source. It has been shown that the system without control cannot guarantee a stationary sending rate. As the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller using polynomial function is proposed to delay the onset of undesirable Hopf bifurcation. Numerical simulation results confirm that the new feedback controller using time delay is efficient in controlling Hopf bifurcation. This approach can be extended to study higher dimensional delay differential equations.

scholarly journals On the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji chaotic system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jianping Shi ◽  
Liyuan Ruan
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaotic System ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Delay Systems ◽  
Feedback Gain ◽  
Stability Of Equilibrium ◽  
Delayed Feedback Controller

Abstract In this paper, we study the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar–Gejji (BG) chaotic system. Since the current study on Hopf bifurcation for fractional-order delay systems is carried out on the basis of analyses for stability of equilibrium of its linearized approximation system, it is necessary to verify the reasonability of linearized approximation. Through Laplace transformation, we first illustrate the equivalence of stability of equilibrium for a fractional-order delay Bhalekar–Gejji chaotic system and its linearized approximation system under an appropriate prior assumption. This semianalytically verifies the reasonability of linearized approximation from the viewpoint of stability. Then we theoretically explore the relationship between the time delay and Hopf bifurcation of such a system. By introducing the delayed feedback controller into the proposed system, the influence of the feedback gain changes on Hopf bifurcation is also investigated. The obtained results indicate that the stability domain can be effectively controlled by the proposed delayed feedback controller. Moreover, numerical simulations are made to verify the validity of the theoretical results.

scholarly journals CONTROLLING STOCHASTIC OSCILLATIONS CLOSE TO A HOPF BIFURCATION BY TIME-DELAYED FEEDBACK

2005 ◽  
Vol 05 (02) ◽  
pp. 281-295 ◽  
Author(s):  
E. SCHÖLL ◽  
A. G. BALANOV ◽  
N. B. JANSON ◽  
A. NEIMAN
Keyword(s):  
Hopf Bifurcation ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Deterministic System ◽  
Control Force ◽  
Stochastic Delay ◽  
Power Spectral ◽  
Delay Differential ◽  
Stochastic Oscillations ◽  
Time Delayed Feedback

We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.

scholarly journals Anti-Swing Control of Gantry and Tower Cranes Using Fuzzy and Time-Delayed Feedback with Friction Compensation

2005 ◽  
Vol 12 (2) ◽  
pp. 73-89 ◽  
Author(s):  
H.M. Omar ◽  
A.H. Nayfeh
Keyword(s):  
Fuzzy Logic Controller ◽  
Mapping Method ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Delayed Feedback Controller ◽  
Identification Technique ◽  
Rotational Motions ◽  
Load Swing ◽  
Gantry Cranes ◽  
Time Delayed Feedback

We designed a feedback controller to automate crane operations by controlling the load position and its swing. First, a PD tracking controller is designed to follow a prescribed trajectory. Then, another controller is added to the control loop to damp the load swing. The anti-swing controller is designed based on two techniques: a time-delayed feedback of the load swing angle and an anti-swing fuzzy logic controller (FLC). The rules of the FLC are generated by mapping the performance of the time-delayed feedback controller. The same mapping method used for generating the rules can be applied to mimic the performance of an expert operator. The control algorithms were designed for gantry cranes and then extended to tower cranes by considering the coupling between the translational and rotational motions. Experimental results show that the controller is effective in reducing load oscillations and transferring the load in a reasonable time. To experimentally validate the theory, we had to compensate for friction. To this end, we estimated the friction and then applied a control action to cancel it. The friction force was estimated by assuming a mathematical model and then estimating the model coefficients using an off-line identification technique, the method of least squares (LS).

Stability and Bifurcation Control in a Fractional Predator–Prey Model via Extended Delay Feedback

2019 ◽  
Vol 29 (11) ◽  
pp. 1950150 ◽  
Author(s):  
Chengdai Huang ◽  
Huan Li ◽  
Tongxing Li ◽  
Shijun Chen
Keyword(s):  
Fractional Order ◽  
Delayed Feedback ◽  
Feedback Controller ◽  
Bifurcation Control ◽  
Feedback Gain ◽  
Feedback Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Delayed Feedback Controller ◽  
Uncontrolled System

This paper explores the bifurcation control of a fractional predator–prey system with an active extended delayed feedback controller. Delay-induced bifurcations criteria for such an uncontrolled system are firstly derived by selecting time delay as a bifurcation parameter. Then, an extended delayed feedback controller is cleverly devised to control Hopf bifurcation for the proposed system. It means that the bifurcation dynamics can be efficaciously controlled for a given system with the adjustment of the fractional order, feedback gain and extended feedback delay provided that the remnant parameters are fixed. The obtained results significantly extend the preceding studies concerning bifurcation control of delayed fractional-order systems. To verify the correctness of the established theory, some numerical results are presented.

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