TWO-TO-ONE RESONANT HOPF-HOPF BIFURCATIONS IN A NONLINEAR OSCILLATOR INVOLVING TIME DELAYS

• 作 者: J.C.Ji;N.Zhang;
• 机 构: School of Electrical,Mechanical and Mechatronic Systems,Faculty,of Engineering and IT,University of
• 出 处: The Third International Conference on Dynamics,Vibration and
• 发表日期: 2010年期

　　Stability and dynamics of nonlinear oscillators involving time delays have received considerable interest [1-4].Presence of time delays in the feedback control may induce instability and complex behaviour of the controlled sy, stem.It was shown that the trivial equilibrium of the corresponding autonomous system may lose its stability via a subcritical or a supercritical Hopf bifurcation and regain its stability via a reverse subcritical or a supercritical Hopf bifurcation as the time delay increases.An interaction of two Hopf bifurcations may occur when the two critical time delays corresponding to two Hopf bifurcations have the same value, which may result in a non-resonant bifurcation of co-dimension two.In the vicinity of non-resonant Hopf bifurcations of the trivial solution, the presence of a periodic excitation can induce complicated behaviour of the controlled system, when the frequency of the external excitation and the frequencies of the two Hopf bifurcations satisfy a certain relationship.