Basins and bifurcations of a delayed feedback control system and its experimental verification for a DC bus circuit

The present study deals with the basins of the equilibrium points embedded within the normal forms of Bogdanov-Takens bifurcation with delayed feedback control. It is numerically shown that the unstable periodic orbit that coexists with the equilibrium point stabilized by delayed feedback control is associated with the basin of the stabilized point. The relation between the periodic orbit and the basin indicates that for enlarging the basin, a homoclinic bifurcation for the orbit and a saddle point can provide useful information for the design of delayed feedback controllers. These results are experimentally confirmed in a real direct-current bus circuit that has dynamics similar to that of the normal form .

Automated summary

This study experimentally confirms the relationship between the unstable periodic orbit and the basin of the stabilized equilibrium point under delayed feedback control, providing useful insights for the design of delayed feedback controllers.