as a perturbative effect from general relativity. Damour and Esposito-Farèse referred to this nonperturbative strong-field effect as “spontaneous scalarization” in analogy to the spontaneous magnetization of the ferromagnets.

In this paper, we investigate spontaneous scalarization in detail with the technique of catastrophe theory. A many-parameter version of the turning point method [@katz1978; @katz1979; @sorkin1981; @sorkin1982] is used as a tool of a stability analysis of equilibrium solutions. The stability analysis of boson stars in scalar-tensor gravity via catastrophe theory in the case of one-dimensional control space was done in [@cs1997; @tls1997]. Catastrophe types of neutron star equilibrium solutions are classified as fold and cusp catastrophes. The occurrence of the cusp catastrophe depends on the choice of the coupling function. Spontaneous scalarization is classified as the cusp catastrophe. From this catastrophic feature, we conclude that the stable configuration of the neutron star may change discontinuously as the baryon number of the star or the asymptotic value of the scalar field changes continuously. The behavior of the scalar charge around the cusp point is explained by catastrophe theory. For the coupling function considered here, when the asymptotic value of the scalar field is such that the theory agrees with general relativity in 