Local bifurcations in the symmetric model of selection with fertility differences

The analysis of difference equations in population dynamics is frequently confined to the calculation of fixed points and the determination of their stability. In general it is not possible to deduce much about the global behavior of the system from such information. This paper presents a study of the bifurcations of fixed points in the symmetric model of selection with fertility differences. Equivalent methods can be applied to other continuous and discrete models to study the dynamics in the vicinity of fixed points in a systemic way and as a first step in an analysis of the global dynamics.