The study of complex systems is essential in many scientific fields for safety, reliability, and security reasons. These systems are increasingly complex and often hybrid (with continuous behaviors in discrete modes), making modeling tasks more difficult. Each design requires a tradeoff between acceptable computation time and good precision. Simulations using numerical methods often sacrifice time efficiency for more precise results, but this choice can show its limits on complex systems. Qualitative reasoning techniques were proposed to sacrifice precision and knowledge to improve speed and generality. They are especially used in diagnosis and fault isolation. Eventually, abstraction methods such as interval propagation or flow-pipe execution emerged in what we now call semi-qualitative simulation, mainly used for precision and property proving. This article proposes an approach that bridges qualitative analysis and numerical simulation methods. It consists in building a qualitative model of a system that is used as a map of its behavior in various regions of its state space to improve the efficiency of its simulation. Therefore, the joint use of models of different natures helps analyze the system's behavior.