Dynamics of an interacting quintom dark energy model in four scenarios and statefinder diagnostic

Abstract This paper investigates the dynamical behavior of a quintom dark energy model, which combines quintessence and phantom scalar fields, across four distinct interacting scenarios: (I) quintessence-matter interaction, (II) phantom-matter interaction, (III) coupled quintessence-phantom-matter interaction, and (IV) intra-dark energy interaction (quintessence-phantom energy exchange). By constructing autonomous dynamical systems for each case, we analyze the stability of critical points and evaluate the cosmological evolution using the statefinder diagnostic pair $$\{r, s\}$$ { r , s } . The exponential potentials for both scalar fields and interaction terms proportional to the matter density $$(Q_1, Q_2)$$ ( Q 1 , Q 2 ) are adopted to derive fixed points, revealing that all scenarios admit late-time phantom-dominated attractors, consistent with accelerated expansion. Notably, interactions between dark sectors significantly alter transient regimes: energy transfer from dark matter to dark energy prolongs matter-quintessence coexistence phases, while reverse transfer accelerates phantom dominance. The statefinder diagnostic, however, fails to distinguish interactions due to overlapping $$s-r$$ s - r trajectories across cases. Numerical simulations further demonstrate epochs of negative phantom energy density in scenarios involving phantom coupling, linked to non-physical fixed points. These results highlight quintom’s flexibility in mimicking observed dark energy behavior while emphasizing the limited discriminatory power of $$\{r, s\}$$ { r , s } for coupling-specific dynamics. The study underscores the role of interactions in alleviating cosmic coincidence problems and shaping multi-phase cosmic histories.