CAJ | 학술논문

为了控制周期系数微分系统平衡点失稳后的分岔行为，基于Floquet-Lyapunov理论，将控制常系数系统分岔行为的方法（线性法、参数法、平移法）应用于一类具有周期系数的力学微分系统，设计了相应的控制器，研究了其控制平衡点分岔行为的有效性。研究结果表明：平移法不能有效控制周期系数微分系统的平衡点失稳后发生的Flip分岔和Hopf分岔行为。若平衡点失稳发生Flip分岔形成周期2点，可分别采用线性法和参数法将周期2点控制到周期1点；若平衡点失稳发生Hopf分岔形成Hopf圈，可分别采用线性法和参数法将Hopf圈控制到周期1点。
위료공제주기계수미분계통평형점실은후적분차행위，기우Floquet-Lyapunov이론，장공제상계수계통분차행위적방법（선성법、삼수법、평이법）응용우일류구유주기계수적역학미분계통，설계료상응적공제기，연구료기공제평형점분차행위적유효성。연구결과표명：평이법불능유효공제주기계수미분계통적평형점실은후발생적Flip분차화Hopf분차행위。약평형점실은발생Flip분차형성주기2점，가분별채용선성법화삼수법장주기2점공제도주기1점；약평형점실은발생Hopf분차형성Hopf권，가분별채용선성법화삼수법장Hopf권공제도주기1점。
In order to control the bifurcation behavior at the equilibrium point of the differential system with periodic coefficients losing its stability,the methods for bifurcation control for the dynamical system with constant coefficients, such as using the linear controller, parameter method, and translation,were applied to a mechanical system with periodic coefficients by the Floquet-Lyapunov theory. Then,the related controllers were designed,and its validity in controlling the bifurcation behavior at the equilibrium point was tested through numerical calculation. The results show that translation is invalid to control the Flip and Hopf bifurcations at the equilibrium point in mechanical system with periodic coefficients. When a 2-periodic point is generated by the period-doubling Flip bifurcation at the unstable equilibrium point,either of the linear controller and the parameter method can be used to control the 2-periodic point back to a 1-periodic point. When a Hopf circle is generated by Hopf bifurcation after the equilibrium point loses its stability,the linear controller and the parameter method are all effective for controlling the Hopf circle to a 1-periodic point.