Indeterminate secondary Hopf bifurcations in nonlinear oscillators

摘要

A forced Van der Pol-type oscillator which exhibits secondary Hopf bifurcations is examined. Subcritical secondary Hopf bifurcations can arise when an unstable torus coalesces with a stable periodic cycle giving a jump to a disconnected attractor. We show that under the variation of a control parameter in the direction of instability indeterminate subcritical secondary Hopf bifurcations may occur where the outcome is extremely sensitive to any finite perturbation given to the system.