CAJ | 학술논문

考虑含参数激励的广义Van der Pol方程的Hopf分岔与控制问题。通过设计线性位移和速度时滞反馈控制器构造了受控系统，着重研究了控制器对该类参数激励系统的1/2亚谐共振的分岔响应控制。采用多尺度法从理论上推导出时滞动力系统的分岔响应方程，并进一步得到Hopf 分岔的存在条件。通过数值模拟，验证了所设计的控制器不仅能控制极限环的幅值，也能控制Hopf 分岔的产生。
고필함삼수격려적엄의Van der Pol방정적Hopf분차여공제문제。통과설계선성위이화속도시체반궤공제기구조료수공계통，착중연구료공제기대해류삼수격려계통적1/2아해공진적분차향응공제。채용다척도법종이론상추도출시체동력계통적분차향응방정，병진일보득도Hopf 분차적존재조건。통과수치모의，험증료소설계적공제기불부능공제겁한배적폭치，야능공제Hopf 분차적산생。
Hopf bifurcation and controlling of a generalized Van der Pol equation with parameter excitation are studied .The delayed feedback controller of linear displacement and velocity is designed to control the system .The paper is devoted to the study of the bifurcation response controlling of 1/2 harmonic resonance of the system .Bifurcation response equation of the time-delays dynamic system is obtained in theory by multiple scale method .Moreover , condition of the existence of Hopf bifurca-tion is also obtained .Numerical simulations show that the controller can control the bifurcation as well as the amplitude of limit cycle.