Bifurcation and stability analysis of commensurate fractional-order van der Pol oscillator with time-delayed feedback

2019 ◽  
Vol 94 (10) ◽  
pp. 1615-1624
Author(s):  
Jufeng Chen ◽  
Yongjun Shen ◽  
Xianghong Li ◽  
Shaopu Yang ◽  
Shaofang Wen
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Bifurcation And Stability ◽  
Time Delayed Feedback

scholarly journals Primary Resonance of van der Pol Oscillator under Fractional-Order Delayed Feedback and Forced Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jufeng Chen ◽  
Xianghong Li ◽  
Jianhua Tang ◽  
Yafeng Liu
Keyword(s):  
Analytical Solution ◽  
Fractional Order ◽  
Approximate Analytical Solution ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Similar System ◽  
Forced Excitation

The primary resonance of van der Pol oscillator under fractional-order delayed negative feedback and forced excitation is studied. Firstly, the approximate analytical solution is obtained based on the averaging method, and it could be found that the fractional-order delayed feedback has not only the property of delayed velocity feedback but also that of delayed displacement feedback. Moreover, the amplitude-frequency equation for the steady-state solution is established, and its stability conditions are also obtained. Then, the results of the approximate analytical solution and numerical integration are compared and analyzed. The agreement between the two methods is very high, so that the correctness and accuracy of the approximate analytical solution are verified. Finally, the effects of all the parameters in the fractional-order delayed feedback on the amplitude-frequency curves are analyzed. It could be concluded that fractional-order delayed feedback has important influences on the dynamical behavior of van der Pol oscillator, which is very significant to the optimization and control of a similar system.

Stationary Response of Duffing-van der Pol Oscillator with Delayed Feedback Control under Wide-Band Noise Excitation

2013 ◽  
Vol 300-301 ◽  
pp. 1518-1524
Author(s):  
Peng Lin ◽  
Chang Shui Feng ◽  
Qiao Yi Wang
Keyword(s):  
Feedback Control ◽  
Wide Band ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Van Der Pol ◽  
Stationary Response ◽  
Wide Band Noise ◽  
Time Delayed Feedback

The stationary response of Duffing-van der Pol oscillator with time-delayed feedback control under wide-band noise excitations is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method. Finally, the stationary response of the system is obtained by solving the Fokker-Plank-Kolmogorov equation associated with the averaged Itô equation. The effect of time delay in feedback control force on the response is analyzed. The theoretical results are well verified through digital simulation.

Analysis of fractional order Bonhoeffer–van der Pol oscillator

2008 ◽  
Vol 387 (2-3) ◽  
pp. 418-424 ◽  
Author(s):  
V. Gafiychuk ◽  
B. Datsko ◽  
V. Meleshko
Keyword(s):  
Fractional Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol
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