First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation

2010 ◽  
Vol 389 (24) ◽  
pp. 5557-5562 ◽  
Author(s):  
Jiaorui Li ◽  
C.S. Feng
Keyword(s):  
Feedback Control ◽  
Business Cycle ◽  
Wide Band ◽  
Random Excitation ◽  
Delayed Feedback Control ◽  
Cycle Model ◽  
First Passage ◽  
First Passage Failure ◽  
Business Cycle Model ◽  
Time Delayed Feedback

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

2013 ◽  
Vol 302 ◽  
pp. 717-722 ◽  
Author(s):  
Ting Zhang ◽  
Chang Shui Feng ◽  
Qiao Yi Wang
Keyword(s):  
Feedback Control ◽  
First Passage Time ◽  
Wide Band ◽  
Reliability Function ◽  
Passage Time ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Delayed Feedback Control ◽  
Control Force ◽  
First Passage

The first passage type reliability 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, from which a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the conditional mean of the first passage time are established. Finally, the conditional reliability function and the conditional mean of first passage time are obtained by solving these equations together with suitable initial condition and boundary conditions. The effect of time delay in feedback control force on the reliability is analyzed. The theoretical results are well verified through digital simulation.

scholarly journals Study on the Business Cycle Model with Fractional-Order Time Delay under Random Excitation

Entropy ◽  
2017 ◽  
Vol 19 (7) ◽  
pp. 354 ◽  
Author(s):  
Zifei Lin ◽  
Wei Xu ◽  
Jiaorui Li ◽  
Wantao Jia ◽  
Shuang Li
Keyword(s):  
Time Delay ◽  
Business Cycle ◽  
Fractional Order ◽  
Random Excitation ◽  
Cycle Model ◽  
Business Cycle Model ◽  
The Business Cycle
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