Human designed systems are growing in complexity, with increasing numbers of components and behavior combinations, resulting in more emergent and unintended behaviors evident in operations. This thesis explores various behavior modeling approaches and their potential for exposing emergent behaviors, highlighting trends and modeling approaches. The report defines key concepts and provides a context for a comparative analysis of approaches. In particular, this report assesses a relatively new approach to behavior and architecture modeling, Monterey Phoenix MP, and compares it with Petri nets, a well-established method. The comparison involves a simple communication process between two components, which is modeled and compared to an equivalent Petri net model. Shared outcomes involve a successful communication between the components and failure modes of the components not receiving or processing data. The models produce identical state space results. The combined state space graph of the Petri model allowed a quick assessment of all potential states but was more cumbersome to build than the MP model. A comparison of approaches charts the modeling methods against the key concepts, revealing the differences among methods, contrasted with the aspects of MP.