Considering the voltage mode controlled flyback converter as the example

this paper studies Hopf bifurcation and quasi-periodicity phenomena in isolated switching converters.The discrete map of the system is derived based on total ampere-turns.Using stroboscopic sampling

bifurcation diagram is obtained with the control period as the bifurcation parameter.Hopf bifurcation phenomenon is studied by calculating the eigenvalues of the period-1 orbit as the equilibrium point loses its stability.The correct expression of natural period with the transformer is presented and the relationship between natural period and control period at Hopf bifurcation point is explained.The rotation number is used to distinguish the evolvement of quasi-periodicity and frequency locking phenomena.The embodiments of the Farey principle

devil's staircase and the expression of rotation number of quasi-periodicity are investigated as well.Finally

experimental results show that the theoretical analysis is correct.