from the spatial derivative in Eq. (\[eq:fieldeq2\]) has a contribution to stabilize the solution. By these two competing effects, the stability of the trivial configuration $\varphi=0$ against spontaneous scalarization is governed. For a detailed analysis of the stability of the trivial configuration, see [@harada1997].

If spontaneous scalarization occurs, the effective gravitational constant, which is $A^2(\varphi)=\exp(\beta\varphi^2)$ in the sense of the inverse of the Brans-Dicke scalar field, becomes considerably smaller than unity. Thereby the gravitation becomes weaker and a considerably larger mass than in general relativity can be supported by the lower matter pressure than in general relativity.

Summary and Discussions
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The behavior of the equilibrium solutions of neutron stars in scalar-tensor theories of gravitation shows a catastrophic feature, which is characterized by a discontinuous change of the system. When we consider a function $A(\varphi)$ of the form $A(\varphi)=\exp(\frac{1}{2}\beta \varphi^2)$, the catastrophe types are classified as fold and cusp catastrophes. The appearance of the cusp catastrophe depends on whether $\beta\agt-4.35$ or $\beta\alt-4.35$. From the fact that those types of catastrophes are structurally stable, it is expected that they would be seen in a wide class of coupling functions.

For $\beta\agt-4.35$, the fold catastrophe on the two-dimensional control space does occur. 