Dynamic physics-based models of resistive switching devices are of great interest for the realization of complex circuits required for memory, logic and neuromorphic applications. Here, we apply such a model of an electrochemical metallization (ECM) cell to complementary resistive switches (CRSs), which are favorable devices to realize ultra-dense passive crossbar arrays. Since a CRS consists of two resistive switching devices, it is straightforward to apply the dynamic ECM model for CRS simulation with MATLAB and SPICE, enabling study of the device behavior in terms of sweep rate and series resistance variations. Furthermore, typical memory access operations as well as basic implication logic operations can be analyzed, revealing requirements for proper spike and level read operations. This basic understanding facilitates applications of massively parallel computing paradigms required for neuromorphic applications.