Excitation spectra are commonly used to study relationship between molecular structure of fluorescent substances and energy transfer during the fluorescence process. It is generally taken for granted that the excitation spectrum of the sample is equivalent to its absorption spectrum, even a copy of the latter. However, exceptions have been found in many cases. Considering various factors that affect the excitation spectra of solution comprehensively, a model has been established to study the behavior of the excitation spectra. After analyzing the model mathematically, including introducing catastrophe theory, we came into the following conclusions: As far as the topological properties are concerned, the excitation spectra are the same as its absorption spectra, provided the concentration of the substance is below a threshold. However, when the concentration is beyond the threshold, the excitation spectra undergo a series of topological saltation, leading to significant a deviation from the absorption spectra. Comparative studies of both excitation and absorption spectra of naphthalene dissolved in n-hexane confirmed the above hypothesis.