Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity.
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
Song
Yongli
Y
Department of Mathematics, Tongji University, Shanghai 200092, China.
Zhang
Tonghua
T
Tadé
Moses O
MO
D000465:Algorithms; D003198:Computer Simulation; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*