We investigate the phase-space dynamics of the Barrow Holographic Dark Energy (BHDE) model in a flat Friedmann-Lemaître-Robertson-Walker (FLRW) Universe, considering the non-interacting scenario between dark energy and dark matter. By expressing the cosmological evolution as a dynamical system using suitable dimensionless variables, we identify the critical points and analyze their stability. The phase-line and stream plots illustrate the trajectories of the system, revealing that the Universe evolves naturally from an early-time matter-dominated epoch to a late-time dark energy-dominated accelerated expansion. The stable attractor corresponding to the dark energy-dominated phase confirms the viability of the BHDE model in describing the observed cosmic acceleration without requiring interaction between dark sectors. In addition to the dynamical investigation, we perform an observational analysis using the latest Cosmic Chronometer, DESI DR2, and Pantheon+ datasets to constrain the model parameters and examine the consistency of the non-interacting BHDE model with current cosmological observations. These results highlight the robustness of the non-interacting BHDE framework as a candidate for explaining late-time cosmological dynamics.
Sudharani et al. (Wed,) studied this question.