CAJ | 학술논문

研究了一个具有线性和非线性时滞反馈的极限环振子系统1∶3共振双Hopf分岔。通过应用多尺度方法，得到了该1∶3共振的复振幅方程，并通过将其复振幅设为极坐标-笛卡尔混合形式，将其复振幅方程转化为一个三维的实振幅系统。通过研究其实振幅方程，对系统在有非线性时滞反馈和无非线性时滞反馈两种情况下的动力学行为进行了分类和比较。结果显示，在两种情形下，系统有完全不同的动力学行为。
연구료일개구유선성화비선성시체반궤적겁한배진자계통1∶3공진쌍Hopf분차。통과응용다척도방법，득도료해1∶3공진적복진폭방정，병통과장기복진폭설위겁좌표-적잡이혼합형식，장기복진폭방정전화위일개삼유적실진폭계통。통과연구기실진폭방정，대계통재유비선성시체반궤화무비선성시체반궤량충정황하적동역학행위진행료분류화비교。결과현시，재량충정형하，계통유완전불동적동역학행위。
A 1∶3 resonant double Hopf bifurcation occurring in a limit cycle oscillator under time delayed linear and nonlinear feedbacks was studied .By using the method of multiple scales , the complex amplitude equations of 1∶3 resonance were obtained .By letting the complex amplitudes as a mixed polar-Cartesian form, the complex amplitude equations were reduced to a three dimensional real amplitude equations .Then the dynamics around the 1∶3 resonant double Hopf bifurcation point was classified in two cases separately .Comparing the two classifications , it was found that there are completely different dynamics in two cases .