Hopf bifurcation and related stability problems for periodic differential systems.

This paper deals with 2π-periodic one parameter differential systems in the plane. Those systems all admit the null solution which is asymptotically stable for a fixed value, say μ=0, and completely unstable for μ>0 small. We find that for the perturbed systems 2π-periodic solutions occur only if another parameter ε which regulates the angular velocity is involved. In any other case an annulus which is asimptotically stable replaces the 2π-periodic solutions.