The evolution of heterogeneous traffic flow stability is needed to be analyzed under different traffic management strategies. In this paper, the lane management strategy and platoon management strategy were proposed for the heterogeneous traffic flow composed of Connected and Automated Vehicles (CAV) and Human Manual Vehicles (HMV). The traffic flow assignment model for the lane management strategy and the calculation method of platoon size for the platoon management strategy were constructed, respectively. Moreover, the Lyapunov Theory was used to develop a framework for the analysis of the traffic flow stability based on the follow-car model of CAV and HMV. A criterion of the heterogeneous traffic flow stability was then proposed to compare the evolution mechanism for different management strategies. The results showed that the heterogeneous traffic flow could be stable, when the speed was higher than 23.12m/s or the CAV permeability was higher than 92%. The heterogeneous traffic flow could remain stable, when the permeability was lower than 60% under the lane management strategy, and the stability of the general lane deteriorates gradually with the increase of the permeability. With the vehicle platoon control algorithm, the heterogeneous traffic flow could be in a stable state with the permeability higher than 19%. This research indicates that CAV random mixing on the road is prone to greatly deteriorating the stability of traffic flow but it can be significantly improved enforcing the lane management and formation control. Among them, the stability domain of the fleet management strategy is optimal, and that of the lane management strategy is better than that of the no agglomeration strategy.