一类时滞非线性相对转动系统的Hopf分岔与周期解的稳定性

Hopf bifurcation and stability of periodic solutions in a nonlinear relative rotation dynamical system with time delay

讨论了一类时滞非线性相对转动系统的Hopf分岔现象,给出了系统产生Hopf分岔的临界时滞条件,利用多尺度法研究了系统在主共振情况下时滞参数对分岔方向和周期解稳定性的影响,最后,用数值模拟对所得结论进行验证.

Hopf bifurcation in a nonlinear relative-rotation system with time delay is considerd, and the critical time delay associated with Hopf bifurcation is found. The time delay＇s influence on the direction and stability of bifurcation are analyzed under the primary resonance condition with the aid of multiple scales. Finally, numerical simulations are performed to verify the analytical results.