Cosmological dynamics of interacting dark matter-dark energy in generalized Rastall gravity

In this work, we investigate late-time interacting cosmologies within the framework of generalized Rastall gravity, where the interaction arises naturally from the non-conservation of the energy-momentum tensor. We formulate the background evolution of the dark sector as an autonomous dynamical system, defining interaction terms Q1=αf˙ and Q2=−f˙(1+α), with α a constant parameter and f a time-dependent function. Three interaction scenarios are studied: f∝ρm, f∝ρde, and f∝ρm+ρde, assuming a constant dark-energy equation-of-state parameter wde. For each scenario, we derive the closed dynamical system in terms of the density parameters (Ωde, Ωm), identify its fixed points, and analyze their stability across the parameter space. In this context, the phase space exhibits standard cosmological dynamics: an unstable radiation point, a transient matter saddle, and a stable late-time attractor with accelerated expansion. In addition, we perform a joint likelihood analysis using Cosmic Chronometers, PantheonPlus, and DESI data to obtain marginalized parameter estimates at the 68% and 95% confidence levels, constraining the parameter space in each interaction model.