Cosmological evolution and late-time attractors in axion-monopole interacting dark energy

We investigate the cosmological dynamics of axion-monopole interacting dark energy, examining whether a microscopically motivated dark-sector interaction can sustain stable late-time acceleration. In particular, magnetic monopoles constitute dark matter and an ultralight axion contributes to dark energy, with their interaction arising from the Witten effect through field-dependent dyon masses. We formulate the autonomous system, classify its critical points and stability, and investigate the evolution analytically and numerically. We find that stable de Sitter attractors at finite positive Hubble parameter require a positive cosmological constant and correspond to axion-potential minima, whereas those at maxima are unstable. Nevertheless, transient axion-driven acceleration remains possible without an explicit cosmological constant. Furthermore, the interaction induces matter-era tracking, namely an attracting slow-drift regime rather than an exact critical point. The interaction-effective dark-energy equation of state can cross the phantom divide, although the physical equation of state remains non-phantom. Extending the analysis to the full Bogomol'nyi-Prasad-Sommerfield dyon mass, we find that the main dynamical features persist, while the field evolution and interaction strength depend on the microscopic dyon properties. Our results demonstrate how a microscopically motivated dark-sector interaction can give rise to distinctive cosmological evolution and effective dark-energy behavior.