Dynamical System Analysis of Interacting Holographic and Modified Ricci Dark Energy Models

In this work, we study the cosmological dynamics of interacting dark energy models in the framework of holographic and modified holographic Ricci dark energy. Different interaction terms between dark matter and dark energy are analyzed to examine how they influence the evolution of the universe. The cosmological field equations are transformed into an autonomous dynamical system using suitable change of variables, and the corresponding critical points are obtained. The stability of the critical points is examined using linear stability theory. The results show that different choices of interaction lead to different cosmological behaviors. In particular, nonlinear interaction terms give more diverse dynamics than linear ones and can lead to stable late-time attractor solutions for suitable values of the model parameters. The evolution of the equation of state parameter and the deceleration parameter is also examined. It is shown that the model can describe an accelerated universe and may allow crossing of the phantom barrier for suitable parameter values. Therefore, we have studied that interacting holographic and modified Ricci dark energy models with suitable interaction terms can be used to explain the late-time accelerated expansion of the universe.