In Chap. 1 we considered the tangential systems \(\mathscr {N}(c)\) and \(\mathscr {N}_{(1,4)HG}[x_1 = c]\) of the Pearcey system and the (1,4) hypergeometric system, respectively, and observed that these tangential systems have periods. Then in Chap. 2 we verified that these periods are defined through the bicharacteristics of their Borel transforms and also expressed as contour integrals on the Riemann surface of the characteristic root. In this chapter we discuss the relationship of these periods with the Stokes geometry and the periodic structure for singularities of solutions of their Borel transforms in a more detailed manner. First, for \(\mathscr {N}(c)\) we introduce its perturbed system \(\widetilde {\mathscr {N}(c)}\) and consider its bicharacteristic chain to show that there exist additional periods and virtual turning points for \(\widetilde {\mathscr {N}(c)}\) which are associated with a non-hereditary turning point of \(\mathscr {N}(c)\) and do not originate from the virtual turning points of the original Pearcey system. We also discuss the relationship between such additional virtual turning points and the Stokes geometry. Then, for \(\mathscr {N}_{(1,4)HG}[x_1 = c]\) we show that its perturbed system also has additional periods similarly to \(\mathscr {N}(c)\) and discuss their relationship with the degeneration of the Stokes geometry. Finally, in Sect. 3.4 we derive connection formulas related to the leaf-type and tadpole-type configurations that appeared in Sect. 1.5 .