Inspired by the well-studied ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$ model, we propose and investigate a class of dynamical dark energy models that evolve from a negative cosmological constant, transitioning to a positive value at low redshifts. Specifically, we introduce a dark energy framework based on a generalized ladder-step function for the cosmological constant. Furthermore, we present two additional models in which the cosmological constant undergoes a smooth sign change at a specified redshift. We provide a detailed discussion of the construction and theoretical properties of these models, analyzing their background cosmological evolution using a cosmographic approach and the statefinder hierarchy parameters. Our results are compared with those obtained for the standard $\mathrm{\Lambda }\mathrm{CDM}$ and ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$ models. We also perform a careful analysis of the types of singularities that may arise in these models due to a sign change in the cosmological constant. Notably, we show that a continuous sign change removes the sudden singularity present in the ${\mathrm{\Lambda }}_{\mathrm{s}}\mathrm{CDM}$ model, replacing it with a milder $w$-singularity.

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• Cosmological constant
• Cosmological parameters
• Dark energy
• Singularities In general relativity