Phase space analysis of sign-changing interacting dark energy models in finslerian cosmology

We explore the dynamical behavior of the cosmological model endowed with an energy transfer between pressure-less cold dark matter and dark energy in the Finsler-Randers framework. The interaction forms considered are dependent exclusively on the intrinsic properties of the dark components and allow for energy transfer across these components. We recast the system into an autonomous system by assuming a constant equation of state for the dark energy and perform a phase space analysis to describe the qualitative behavior. The dynamic behavior of the model strongly depends on the interaction term along with the dark energy parameter. The existence of stable late-time attractors represents the accelerated expansion of the universe in these models. The overall behavior based on the qualitative dynamics describes the transiting universe evolution dynamics composed of matter and dark energy dominated phases and thus presents the promising character of the Finslerian geometry-based interacting models. We test the observational viability of the model through parameter estimation using the CC and Pantheon + datasets, which jointly constrain the expansion history from low to high redshift. Moreover, the comparison of the best-fit H ( z ) curves for the individual CC and Pantheon + datasets within the Finsler model is presented.