Active, resistive, nonlinear, uniform, infinite ladder networks

A strictly passive, resistive, nonlinear, uniform, infinite ladder network has a characteristic immittance (v,i)→W(vi) with exactly one fixed point in the voltage-current plane, that fixed point is a saddle point of the first kind and occurs at the origin. However, if `strictly passive´ is replaced by `active´, the number of fixed points can be many. If the series resistances and shunt conductances are continuous functions whose zeros are all distinct and changes-of-sign as well, then the fixed points of W appear in a rectangular pattern in the ( v,i) plane. Moreover, if v₀ is a zero of g and i₀ is a zero of r and if G and R are the derivatives of g and r at v₀ and i₀, respectively, and are both positive or both negative, then (v ₀,i₀) is a saddle point of the first kind. On the other hand, if G and R are of opposite sign, then (v₀,i₀) is a center when -4<GR<0 and a saddle point of the second kind when GR<-4