Sensitivity Analysis of Certain Dynamic Bifurcations

Control systems and other dynamic systems may lose stability at critical points from which bifurcations take place. However, due to the existence of small disturbances or imperfections, the dynamic behaviour of a system-in particular, the stability conditions-may change drastically. This paper is concerned with the imperfection sensitivity of dynamic bifurcations (degenerate or generalized Hopf bifurcations) arising in nonlinear autonomous systems. The analysis is carried out via the unijicalion technique coupled with the intrinsic harmonic balancing procedure. lt has been observed that the sensitivity properties associated with dynamic bifurcations are inherently different from those associated with static bifurcations. However, some similarities concerning the sensitivity curves do exist. A nonlinear feedback control system is analyzed to demonstrate the applicability of the analytic results.