Difference equations can be thought of as the discrete analog of differential equations. They can be used to model systems that evolve in discrete steps, but they also arise directly from differential equations, both in the context of numerical solutions and in the investigation of the stability of periodic solutions. Some of the instabilities and bifurcations of fixed points of difference equations are analogous to those for differential equations, but one type is not—the flip or period-doubling bifurcation, which leads to a solution that alternates between two discrete values.