of equilibrium solutions of neutron stars bifurcates at a point. Beyond this point, the general relativistic branch becomes unstable and another two (degenerate) sequences of equilibrium solutions far from the general relativistic one are stable. This bifurcation point is a cusp point, and the behavior of the scalar charge and scalar susceptibility near the cusp point is explained by the form of the potential function of the cusp catastrophe. At a point on the envelopes other than the cusp point, the fold catastrophe occurs. Since the critical baryon numbers $N^{crit1}$ and $N^{crit2}$ agree, the number of stable equilibrium solutions is 1 for $N<N^{crit3}$, 2 for $N^{crit3}<N<N^{crit2}=N^{crit1}$ and 0 for $N^{crit2}=N^{crit1}<N$. It should be noticed that, for the near critical case $-4.9\alt\beta\alt-4.35$, the structure of the cusp catastrophe does appear although the behavior becomes somewhat more complicated around the maximum baryon number for $\varphi_0\simeq 0$. This complicated feature agrees with the fact that the critical mass against zero-mode instability is not a monotonic function with respect to $\beta$, which is seen in Table I of [@harada1997].

Here we comment on the continuous change of the asymptotic value of the scalar field $\varphi_0$. If we identify $\varphi_0$ with the cosmological value of 