Phase-locking of a harmonically forced self-oscillating system

We present the bifurcation diagram for solutions of the forced Landau equation [d/dt - 1 + i omega + (1 + ic(3))/Psi/(2)]Psi = F-0, for c(3) not equal 0. The bifurcations of the phase locked states (fixed points) are obtained analytically for all parameter values. Bistable regions exist in the bifurcation diagram consisting of phase locked solutions alone as well as a phase locked and a periodic solution, sometimes accompanied by a repelling closed orbit.