scholarly journals Stationary Bifurcation Control for Systems with Uncontrollable Linearization

1999 ◽  
Author(s):  
Taihyun Kim ◽  
Eyad H. Abed
Keyword(s):  
Bifurcation Control ◽  
Stationary Bifurcation

Transitions Through Period Doubling Route to Chaos

1991 ◽  
Author(s):  
R. M. Evan-lwanowski ◽  
Chu-Ho Lu
Keyword(s):  
Period Doubling ◽  
Mirror Image ◽  
Flip Flop ◽  
Physical Systems ◽  
Starting Conditions ◽  
Spatial System ◽  
Stationary Bifurcation ◽  
Extreme Sensitivity ◽  
Route To Chaos ◽  
Parameter Values

Abstract The Duffing driven, damped, “softening” oscillator has been analyzed for transition through period doubling route to chaos. The forcing frequency and amplitude have been varied in time (constant sweep). The stationary 2T, 4T… chaos regions have been determined and used as the starting conditions for nonstationary regimes, consisting of the transition along the Ω(t)=Ω0±α2t,f=const., Ω-line, and along the E-line: Ω(t)=Ω0±α2t;f(t)=f0∓α2t. The results are new, revealing, puzzling and complex. The nonstationary penetration phenomena (delay, memory) has been observed for a single and two-control nonstationary parameters. The rate of penetrations tends to zero with increasing sweeps, delaying thus the nonstationary chaos relative to the stationary chaos by a constant value. A bifurcation discontinuity has been uncovered at the stationary 2T bifurcation: the 2T bifurcation discontinuity drops from the upper branches of (a, Ω) or (a, f) curves to their lower branches. The bifurcation drops occur at the different control parameter values from the response x(t) discontinuities. The stationary bifurcation discontinuities are annihilated in the nonstationary bifurcation cascade to chaos — they reside entirely on the upper or lower nonstationary branches. A puzzling drop (jump) of the chaotic bifurcation bands has been observed for reversed sweeps. Extreme sensitivity of the nonstationary bifurcations to the starting conditions manifests itself in the flip-flop (mirror image) phenomena. The knowledge of the bifurcations allows for accurate reconstruction of the spatial system itself. The results obtained may model mathematically a number of engineering and physical systems.

scholarly journals Bifurcation control of Fitzhugh-Nagumo models

2018 ◽  
Vol 22 (Özel) ◽  
pp. 375 ◽  
Author(s):  
Reşat Özgür DORUK ◽  
Hamza IHNISH
Keyword(s):  
Bifurcation Control

scholarly journals Hopf Bifurcation Control in a Lorenz Type System

2018 ◽  
Vol 06 (08) ◽  
pp. 1704-1719
Author(s):  
P. E. Calderon-Saavedra ◽  
E. Munoz-Aguirre ◽  
J. Alvarez-Mena ◽  
S. Gomez-Perez
Keyword(s):  
Hopf Bifurcation ◽  
Type System ◽  
Bifurcation Control

scholarly journals Research on Principal Resonance Bifurcation Control of Roller System in Corrugated Rolling Mills

2020 ◽  
Vol 56 (7) ◽  
pp. 109
Author(s):  
HE Dongping ◽  
WANG Tao ◽  
XIE Jiaquan ◽  
REN Zhongkai ◽  
LIU Yuanming ◽  
...  
Keyword(s):  
Bifurcation Control ◽  
Principal Resonance ◽  
Rolling Mills ◽  
Roller System ◽  
Resonance Bifurcation

Bifurcation Control in Feedback Systems

2004 ◽  
pp. 205-228 ◽  
Author(s):  
Diego M. Alonso ◽  
Daniel W. Berns ◽  
Eduardo E. Paolini ◽  
Jorge L. Moiola
Keyword(s):  
Bifurcation Control ◽  
Feedback Systems
Sign in / Sign up

Export Citation Format

Share Document