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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… Click to show full abstract
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 .
Journal Title: Nonlinear Dynamics
Year Published: 2021
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