scholarly journals Control of period-doubling bifurcation and chaos in a discrete nonlinear system by the feedback of states and parameter adjustment

2003 ◽  
Vol 52 (4) ◽  
pp. 790
Author(s):  
Luo Xiao-Shu ◽  
Chen Guan-Rong ◽  
Wang Bing-Hong ◽  
Fang Jin-Qing ◽  
Zou Yan-Li ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Bifurcation And Chaos ◽  
Parameter Adjustment

scholarly journals The Application of the Undetermined Fundamental Frequency Method on the Period-Doubling Bifurcation of the 3D Nonlinear System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Gen Ge ◽  
Wei Wang
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Fundamental Frequency ◽  
Three Dimensional ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Cubic Nonlinearity ◽  
Frequency Method ◽  
The Stability ◽  
Second Period

The analytical method to predict the period-doubling bifurcation of the three-dimensional (3D) system is improved by using the undetermined fundamental frequency method. We compute the stable response of the system subject to the quadratic and cubic nonlinearity by introducing the undetermined fundamental frequency. For the occurrence of the first and second period-doubling bifurcation, the new bifurcation criterion is accomplished. It depends on the stability of the limit cycle on the central manifold. The explicit applications show that the new results coincide with the results of the numerical simulation as compared with the initial methods.

scholarly journals Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait

2012 ◽  
Vol 57 (14) ◽  
pp. 1743-1750 ◽  
Author(s):  
Jie Zhao ◽  
XiaoGuang Wu ◽  
XiZhe Zang ◽  
JiHong Yan
Keyword(s):  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Bifurcation And Chaos
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