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• A new route choice principle for mixed traffic flow of autonomous vehicles and inertial human-driven vehicles. • Existence and uniqueness of the fixed point of the proposed day-to-day dynamic traffic assignment model. • Stability and convergence conditions for the proposed day-to-day dynamic traffic assignment model. Autonomous vehicle (AV) technology is likely to bring unprecedented change to existing transport systems due to its potential to enhance safety and efficiency. Nevertheless, before entering a fully AV era, human-driven vehicles (HVs) and AVs are expected to coexist for a long time, during which HVs and AVs could behave differently in route choice. On the one hand, compared with HVs, AVs can acquire more comprehensive traffic information and also process the information more swiftly. On the other hand, HV users may habitually maintain a satisfactory path but not necessarily choose the optimal one to the same destination to save cognitive during daily trips. AV users, however, may not show such behavior on account of the advantages of AVs. To capture these features in the coexistent period, understand their effects on the evolution of daily traffic flow, and provide managerial insights, this study presents a deterministic discrete time day-to-day dynamic assignment model for the mixed HV and AV traffic flows. In which both AV users and HV users choose their path according to their perception, AV users have better perceptual ability than HV users, and bounded behavioral inertia is first introduced to depict the travel behavior that HV users habitually maintain a satisfactory path during daily trips. The existence and uniqueness of the fixed-point and the convergence conditions of the proposed dynamic model are demonstrated and given. Theoretical results are verified in a simple two-path network, the Nguyen-Dupuis network, and the Sioux Falls network, respectively. The interactions between AVs and HVs are explored in the three numerical examples. Our research indicates that the introduction of AVs can reduce the overall travel time of a transport system and increase road capacity. Bounded behavioral inertia of HV users can maintain more HV flows on a better route, brings a more balanced distribution of travel flow on different paths, and facilitate the stability of a whole transport system. [ABSTRACT FROM AUTHOR]