Collaborative multi-actuator systems represent a promising avenue for the development of visionary applications such as robotics, medical appliances, and advanced user interfaces. Among various technologies, Dielectric Elastomer (DE) transducers exhibit synergistic properties conducive to cooperative systems. The same material can fulfill different tasks, such as actuation, sensing, or energy harvesting. Combining multiple DE actuators and DE switches can enable similar soft structures to implement basic logic and storage functions. In this paper, we present a mathematical model for a DE transducer network capable of complex actuation tasks. Drawing from our research on DE sensors and actuators, we have developed a model that integrates DE components to simulate multi-actuator networks. Multiple DE switches are interconnected through logic unit designs to achieve complex electro-mechanical behaviors. We predict the multiple outputs of a single input pulse voltage for a highly integrated inverter system through simulation. It opens more possibilities in the application field of cooperative multi-actuator systems.