While artificial neural networks are regularly employed in modeling the perception of facial and vocal emotion expression as well as in automatic expression decoding by artificial agents, this approach is yet to be extended to the modeling of emotion elicitation and differentiation. In part, this may be due to the dominance of discrete and dimensional emotion models, which have not encouraged computational modeling. This situation has changed with the advent of appraisal theories of emotion and a number of attempts to develop rule-based models can be found in the literature. However, most of these models operate at a high level of conceptual abstraction and rarely include the underlying neural architecture. In this contribution, an appraisal-based emotion theory, the Component Process Model (CPM), is described that seems particularly suited to modeling with the help of artificial neural network approaches. This is due to its high degree of specificity in postulating underlying mechanisms including efferent physiological and behavioral manifestations as well as to the possibility of linking the theoretical assumptions to underlying neural architectures and dynamic processes. This paper provides a brief overview of the model, suggests constraints imposed by neural circuits, and provides examples on how the temporal unfolding of emotion can be conceptualized and experimentally tested. In addition, it is shown that the specific characteristics of emotion episodes can be profitably explored with the help of non-linear dynamic systems theory.