A system of systems(SoS)composes a set of inde-pendent constituent systems(CSs),where the degree of autho-rity to control the independence of CSs varies,depending on dif-ferent SoS types.Key researchers describe four SoS types with descending levels of central authority:directed,acknowledged,collaborative and virtual.Although the definitions have been re-cognized in SoS engineering,what is challenging is the difficulty of translating these definitions into models and simulation envi-ronments.Thus,we provide a goal-based method including a mathematical baseline to translate these definitions into more effective agent-based modeling and simulations.First,we con-struct the theoretical models of CS and SoS.Based on the theo-retical models,we analyze the degree of authority influenced by SoS characteristics.Next,we propose a definition of SoS types by quantitatively explaining the degree of authority.Finally,we recognize the differences between acknowledged SoS and col-laborative SoS using a migrating waterfowl flock by an agent-based model(ABM)simulation.This paper contributes to the SoS body of knowledge by increasing our understanding of the degree of authority in an SoS,so we may identify suitable SoS types to achieve SoS goals by modeling and simulation.