Dynamical system approach of interacting dark energy models in f(R, Tϕ) gravity

We have examined an isotropic and homogeneous cosmological model in f(R, Tϕ) gravity, where R represents the Ricci scalar and Tϕ exhibits the energy momentum tensor’s trace. We examine the stability criteria by performing the dynamical system analysis for our model f(R, Tϕ) = R + 2(aTϕ + b), where a and b are the constants. We derive a set of autonomous equations and find their solutions by assuming a flat potential V0. We assess the equilibrium points from these equations and find the eigenvalues. We analyze the physical interpretation of the phase space for this system. We obtain three stable equilibrium points. We also examine the interaction between the scalar field and dark energy, represented by Q = ψHρde and determine the equilibrium points for this interaction. We identify four stable equilibrium points for this interaction. We calculate the values of the physical parameters for both scenarios at each equilibrium point, indicating the Universe’s accelerated expansion. © 2025 Elsevier B.V., All rights reserved.