Effects of nonlinear interactions on phase portraits and dynamical stability in specific modified gravity

Abstract

Dynamical system analysis is a vital mathematical mechanism for the qualitative study of dynamical models. Cosmological equations governing the dynamics of an isotropic and homogeneous Universe imply dynamical models in the form of differential equations. In the present article, we formulate four models with nonlinear interactions in the theoretical framework of deformed Hořava–Liftshitz and apply the dynamical system analysis to these models to investigate their dynamical stability with phase portraits. Phase portrait trajectories identify the stable steady states for each model, we compute different cosmic parameters at these stable critical points and compare it with the latest observational cosmic data. We find our outcomes are consistent with recent comic observational data, this implies that the theoretical framework under consideration with nonlinear interactions is consistent with current accelerating scenario of the Universe.