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tokens: G. The blue and red solid circles denote the current positions of two example binaries with initial parameters days and , and day and , respectively. Figure 4 shows the distribution of the binaries at end of the evolution with f = 0, 0.02, 0.1, and 0.3, corresponding to either the donor star having evolved to be a WD or the age of the binary exceeding Hubble time. The binaries with orbital periods at the beginning of the second RLOF above the so-called bifurcation period (Pylyser Savonije 1988 , 1989 ) evolve into low-mass binary pulsars (LMBPs), with a helium WD companion (depicted with circles), while those with orbital periods below the bifurcation period evolve into compact LMXBs with substellar companion stars (depicted with triangles). To see how the bifurcation period changes with mass transfer and evaporation, we present the orbital period evolution for five NS binaries with different f values in Figure 5 . It seems that the bifurcation periods are quite close to each other (∼1 day) and increase slightly with increasing f . Figure 4. Distribution of the final orbital period and donor mass under different values of f . The blue and red symbols have the same meanings as in Figure 2 . The solid line is the theoretical – relation of LMBPs given by Tauris Savonije ( 1999 ). Figure 5. Post-AIC evolution of the orbital period under different values of f for five NS binaries. Here denotes the time at AIC. From top to bottom, the initial parameters are: days and , days and , days and , days and , and days and . The solid line in the four panels in Figure 4 is the theoretical relation for LMBPs given by Tauris Savonije ( 1999 ). We can see that if there is no evaporation in the post-AIC evolution, the resulting distribution is well-consistent with the theoretical relation, which is the same as in the LMXB evolution. However, once evaporation is included, the distribution deviate from the theoretical prediction, especially in the case of f = 0.3: for a given , the orbital period is longer than expected. The reason is that in the late stage of the evolution, the orbital evolution and mass loss are mainly driven by evaporation rather than mass transfer via RLOF (see also Jia Li 2016 ). To demonstrate the detailed evolutionary processes, in Figures 6 and 7 , we present two representative examples for the post-AIC binaries, which are marked in Figures 3 and 4 . Figures 6 and 7 correspond to the blue circle with days and , and the red triangle with day and , respectively. Figure 8 compares the rates of AML caused by different mechanisms in the evolutionary paths presented in Figures 6 (left panel) and 7 (right panel). In Figures 6 and 7 , the left panel displays the evolution of the mass transfer rate (black solid line), the evaporative wind loss rate (red line), and the donor mass (blue line). The black dashed line represents the critical mass transfer rate for disk instability. The right panel depicts the evolution of the NS mass (solid line) and