Editing Network analysis (electrical circuits) (section)

===Existence, uniqueness and stability===
An important consideration in non-linear analysis is the question of uniqueness. For a network composed of linear components there will always be one, and only one, unique solution for a given set of boundary conditions. This is not always the case in non-linear circuits.  For instance, a linear resistor with a fixed current applied to it has only one solution for the voltage across it.  On the other hand, the non-linear [[tunnel diode]] has up to three solutions for the voltage for a given current.  That is, a particular solution for the current through the diode is not unique, there may be others, equally valid. In some cases there may not be a solution at all: the question of existence of solutions must be considered.

Another important consideration is the question of stability. A particular solution may exist, but it may not be stable, rapidly departing from that point at the slightest stimulation.  It can be shown that a network that is absolutely stable for all conditions must have one, and only one, solution for each set of conditions.<ref>Ljiljana Trajković, "Nonlinear circuits", ''The Electrical Engineering Handbook'' (Ed: Wai-Kai Chen), pp. 79–81, Academic Press, 2005 {{ISBN|0-12-170960-4}}</ref>