Using degree theory to determine the minimum number of unstable operating points that a nonlinear circuit must possess

It has been shown previously that any structurally stable operating point (i.e., an operating point that does not disappear when the component values are perturbed slightly) of a nonlinear circuit must have an index of either +1 or -1. It is shown here that any operating point that has an index of -1 must be unstable. A simple relationship is derived between the number of operating points with index -1 and with index +1, thereby proving that if a circuit is known to possess n structurally stable operating points (n has been shown previously to be odd), then (n-1)/2 of these operating points must be unstable and hence unobservable for the physical circuit. A special case of this result proves that an bistable circuit must possess at least three operating points