Chemical networks often exhibit emergent, systems-level properties that cannot be simply derived from the linear sum of the individual components. The design and analysis of increasingly complex chemical networks thus constitute a major area of research in Systems Chemistry. In particular, much research is focused on the emergence of functional properties in prebiotic chemical networks relevant to the origin and early evolution of life. Here, we apply a formal framework known as RAF theory to study the dynamics of a complex network of mutually catalytic peptides. We investigate in detail the influence of network modularity, initial template seeding, and product inhibition on the network dynamics. We show that these results can be useful for designing new experiments, and further argue how they are relevant to origin of life studies.