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 (Q₁, Q₂) (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.
Liu et al. (2026) studied this question.