Uniqueness of an equilibrium position

To illustrate the non-existence of a unique equilibrium position, we present two examples.

Figure 46: No equilibrium state

Here there is no equilibrium state. The stabilizing run must and does fail.

Figure 47: Infinite number of equilibrium positions

Here there are a whole range of positions which are equilibrium states. In other words there is an infinite number of equilibrium positions. The stabilizing run finds one of these. The Hold inputs constant methods finds the equilibrium position accessible from the starting position.

Do not think it is always easier to find a steady state solution directly than do a dynamic solution. Often the opposite is true.