The authors introduce real and complex multi-parameter homotopy methods for finding DC solutions of nonlinear circuits. They show, using arguments from algebraic topology and circuit and polynomial examples, that multi-parameter homotopy methods can avoid bifurcation points and folds along solution paths, and find multiple solutions with relative ease. These concepts are illustrated on a third-order polynomial with a cusp, an object with folds and a bifurcation point, and on two circuit examples. Simple, isolated solution points in a compact region are assumed.
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