To study the following characteristics and stability conditions of vehicles on curved roads, this paper builds upon an intelligent driver model (IDM), integrating considerations of factors such as curve radius and super-elevation, and incorporating road mechanics to establish an extended model. By analyzing the influence of curves on traffic flow stability, the study derives stability conditions applicable to both homogeneous and heterogeneous traffic flows comprising human driven vehicles (HDVs), automated vehicles (AVs), and connected automated vehicles (CAVs). Parameter sensitivity analyses and numerical validations are conducted. The findings indicate that traffic flow stability is highest under Condition 2 (). Increasing equilibrium speeds enhances traffic flow stability, while increasing free-flow speeds is detrimental to stability. Moreover, as CAVs penetration rates increase, the stability of mixed traffic flows gradually improves, although increasing maximum platoon sizes may destabilize traffic flows. In homogeneous traffic flows, lower speeds are advantageous for stability at low speeds; for high-speed conditions, stability is optimized at speeds of 29.9 m/s for HDVs, 26.8 m/s for AVs, and 26.9 m/s for CAVs. In mixed traffic flows, stability can be maintained when the penetration rates of CAVs exceed 0.72.