This study addresses the challenge of electric vehicle power battery recycling by proposing a dynamic deposit-refund system (DRS) under the Extended Producer Responsibility (EPR) framework, as an alternative to the conventional static DRS. An evolutionary game model is developed to capture the strategic interactions between local governments and responsible enterprises, incorporating a feedback mechanism where the deposit level is dynamically adjusted based on corporate EPR fulfillment rates. Using system dynamics simulation, the evolutionary paths under both static and dynamic DRS regimes are compared. The results demonstrate that the dynamic DRS effectively eliminates persistent oscillations and guides the system toward a stable equilibrium. Furthermore, by defining an ideal scenario, key factors are identified and prioritized to assist the government in steering the system toward this desired state. These findings offer actionable insights for designing adaptive regulatory mechanisms and fostering a self-sustaining battery recycling ecosystem.