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.
Hopf bifurcation and related stability problems for periodic differential systems / Bernfeld, S. R.; L., Salvadori; Visentin, Francesca. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 116:2(1986), pp. 427-438.
Hopf bifurcation and related stability problems for periodic differential systems.
VISENTIN, FRANCESCA
1986
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.