Dynamical system approach of interacting dark energy models with minimally coupled scalar field

Abstract

We investigated the stability condition of [Formula: see text] gravity theory with interacting and noninteracting models by using dynamical system. We assume the [Formula: see text] function as [Formula: see text], where [Formula: see text] is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is [Formula: see text]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters [Formula: see text] in terms of z and discuss the nature of r–s and r–q plane. For both pairs [Formula: see text] and [Formula: see text] our model represents the [Formula: see text]CDM model. Hence, we determine that our [Formula: see text] model is stable and it satisfies all the observational values.