A bifurcation analysis of a simple electronic circuit (Q1886397)

The authors present a bifurcation analysis of an electronic circuit with a three-dimensional state-space, displaying a cubic nonlinearity realized by a voltage-controlled resistor. They focus on parameter values yielding an equilibrium with an (index-2 nilpotent) double-zero eigenvalue in the linearization. The nonlinear analysis is performed via normal forms in the center manifold. They compute parameter values leading to a codimension-three degenerate Takens-Bogdanov bifurcation. Numerical computations of bifurcation sets are carried out for two nondegenerate, codimension-two Takens-Bogdanov bifurcations organizing saddle-node and Hopf bifurcations together with homoclinic connections; saddle-node bifurcations of periodic orbits stemming from a degenerate Hopf bifurcation can also be observed.