Multi-parameter homotopy methods for finding periodic solutions of nonlinear circuits

This paper applies real and complex multi-parameter homotopy to finding periodic solutions of nonlinear circuits. We show using circuit examples and normal forms coupled with codimension arguments, that multi-parameter homotopy methods can avoid period-doubling and cyclic fold bifurcations along solution paths, and find all solutions along a period-doubling path. We distinguish between circuit-direct and formulation-indirect multiparameter homotopy, and show that the latter (with two real parameters) can avoid period-doubling bifurcations, while the former cannot