A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of...A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of the nonlinear oscillator, feedback controllers were designed. Bifurcation control equations were obtained by using the multiple scales method. And through the numerical analysis, good controller could be obtained by changing the feedback control gain. Then a feasible way of further research of saddle-node bifurcation was provided. Finally, an example shows that the feedback control method applied to the hanging bridge system of gas turbine is doable.展开更多
By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f...By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.展开更多
基金Project(10672053) supported by the National Natural Science Foundation of ChinaProject(2002AA503010) supported by the National High-Tech Research and Development Program of China
文摘A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of the nonlinear oscillator, feedback controllers were designed. Bifurcation control equations were obtained by using the multiple scales method. And through the numerical analysis, good controller could be obtained by changing the feedback control gain. Then a feasible way of further research of saddle-node bifurcation was provided. Finally, an example shows that the feedback control method applied to the hanging bridge system of gas turbine is doable.
基金Supported by the National Natural Sciences Foundation of China(10361006)Supported by the Natural Sciences Foundation of Yunnan Province(2003A0001M)Supported by the Jiangsu "Qing-lanProject" for Excellent Young Teachers in University(2006)
文摘By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.
