<p>Frequency switching dynamical systems have recently garnered significant attention owing to their ubiquitous presence and the distinctive fast-slow dynamics. Previous work have reported that frequency switching can induce divergences for certain switching thresholds, destabilizing the bursting solutions in slowly excited vector field related to transcritical bifurcation. The present study concentrates on the analysis and regulation of the divergence behavior in frequency switching dynamical systems. Based on the same vector field, two necessary conditions for switching divergence are identified, with one being effectively invalidated by rationally adjusting the switching scheme. As a result, the threshold window for divergence is blocked, yielding a set of sliding bursting patterns that hold for any reasonable threshold. Building on this, the influence of the perturbation of excitation frequency on system stability is explored, revealing up to four previously-undocumented divergent modes modulated by the reference excitation frequency. In addition to summarizing the frequency-threshold distribution spectra for each divergent mode under different initial conditions, this research elucidates the underlying dynamical mechanism of the origins and distribution of these divergent modes. This work provides insights into the regulation of switching-induced instability and the novel divergent modes modulated by the reference excitation frequency in frequency switching systems, advancing our understanding of frequency switching dynamics.</p>