Abstract: Existing research on the synthesis of Petri net models focuses on preserving system properties, such as liveness, reachability, and reversibility. Such research overlooked the importance of system behavior relation preservation models. In this paper, we discuss three important connection operations : self-loops, inhibitor arcs and synchronisation, in order to model system behavior characteristics. Their behavior relation formulas have been obtained by two transformations to these operations. Furthermore, we formally prove that these three connection operations satisfy the behavior invariance. These results support a formal tool for dynamic analysis of Petri net models in synthesis process.