ABSTRACT
In Chapter 5, we saw that equilibrium points, or fixed points, are important features of many systems of differential equations. In addition, the local stability of any equilibrium points is significant because it is this property that determines whether solutions of the differential equations that start near to equilibrium will tend towards the equilibrium point, or away from it. Frequently, systems of differential equations contain one or more parameters, that are usually assumed to be constants. A natural question to ask, however, is how do the position and stability of an equilibrium change as one of the parameters of the system is varied. Such a parameter will be called a control parameter to distinguish it from any parameters which remain fixed.
