Parametrized Families of Functions and Bifurcations

Abstract

By a family of functions we mean a collection of functions that are of the same general type. For example we consider the family of linear functions of the form f _m (x) = mx, where m is allowed to vary over the real numbers. The variable m is called a parameter and the family represented by f _m (x) = mx is called a parametrized family. The parameter is usually written as a subscript of the function name. In those cases where the parameter is clear, we will suppress the subscript to simplify notation.