scholarly journals Existence of finite time blow-up solutions in a normal form of the subcritical Hopf bifurcation with time-delayed feedback for small initial functions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kazuyuki Yagasaki
Keyword(s):  
Hopf Bifurcation ◽  
Normal Form ◽  
Finite Time ◽  
Blow Up ◽  
Delayed Feedback ◽  
Subcritical Hopf Bifurcation ◽  
Time Delayed Feedback

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.

Sign in / Sign up

Export Citation Format

Share Document