Self-reproducible DEVS formalism

System reproduction model to the growing system structure can be used to design modeling formalisms for variable system architectures having historical characteristics. We introduce a discrete event system specifications (DEVS)-based extended formalism that a system structure gradually grows through self-reproductions of system components. The proposed formalism is applied to atomic DEVS modeling and coupled DEVS modeling. As extended-atomic DEVS model, atomic self-reproduction (SR) DEVS modeling to a system component makes virtual-child atomic DEVS models. By SR DEVS modeling, a child coupled model can be also reproduced from a parent coupled model. When a system component model reproduces its system component, a child component model can receive its parent model characteristics including determined role or behavior, and include different structure model characteristics. A virtual-child model that has its parent characteristics can also reproduce next child model which may show similar attributes of the grand-parent model.