Dynamical system approach of non-minimal coupling in holographic cosmology

We study the dynamical system approach of non-minimally coupled scalar field to induced gravity on the brane in the framework of holographic cosmology. In this context, we derive the modified Friedmann equation and the equation of motion. The dynamics of this model are studied by rewriting the cosmological field equations in the form of a system of autonomous differential equations. In particular, the analysis is considered by investigating an exponential potential and a monomial form of the non-minimal coupling function. We show that, for sufficient conditions, a past de Sitter attractor solution is obtained in the case of a minimal coupling, meanwhile a future de Sitter attractor solutions is obtained for a conformal coupling and for a non-minimal coupling. (C) 2019 The Authors. Published by Elsevier B.V.