On a global representation of dynamical characteristics in ESS-models

ESS-models are considered in the frame of adequate dynamical systems. This leads to a method of global representation of the dynamical characteristics, which allows for a comprehensive view on the relations among ESS-matrices. As an extension of ESS-models, the concept of ESS-models with changing matrix is introduced, which, in applications, makes use of such global representations. In particular, structurally stable and "catastrophic" cases can be identified and their significance in the context of ESS-models can be clarified. As a complete result for the case of two strategies a surface representation is obtained, which is an analogue to the elementary "cusp catastrophe". These concepts are applied in a model that describes directed evolution of a behavioural component to a certain limit.