We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule;moreover, each agent can change his type to adopt another updating rule once the number he sequentially loses the game at is beyond his upper limit of tolerance. The cooperative behaviors of such heterogeneous systems are then inves-tigated by Monte Carlo simulations. The numerical results show the equilibrium cooperation frequency and composition as functions of the cost-to-benefit ratio r are both of plateau structures with discontinuous steplike jumps, and the number of plateaux varies non-monotonically with the upper limit of tolerance vT as well as the initial composition of agents fa0. Besides, the quantities of the cooperation frequency and composition are dependent crucially on the system parameters including vT, fa0, and r. One intriguing observation is that when the upper limit of tolerance is small, the cooperation frequency will be abnormally enhanced with the increase of the cost-to-benefit ratio in the range of 0