A complex dynamical behaviour called ‘chaos’ is observed in mathematical models expressed in the form of recurrences with non-unique inverses. The attractive limit sets of an endomorphism are located in phase plane domains bounded by segments of critical curves and called absorptive areas. Frequently in such an endomorphism, the sequence of consequents of a point belonging to an initial condition domain have an apparently erratic movement in a bounded domain of the (x, y) plane called a chaotic area. The variation of a parameter can modify the nature of these chaotic areas. Different bifurcations occurring in chaotic areas are described in this paper and are illustrated by the study of examples.