Dynamical Systems analysis of an interacting dark energy model in the Brane Scenario

TL;DR

This paper analyzes the background dynamics of an interacting dark energy model within brane cosmology, using autonomous systems and stability analysis to understand its critical points and classical stability.

Contribution

It introduces a dynamical systems approach to study the stability and critical points of an interacting dark energy model in brane cosmology.

Findings

Identification of critical points and their stability properties.

Analysis of classical stability of the model.

Insights into the evolution of dark energy and dark matter interaction.

Abstract

In this paper, we investigate the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here we consider an homogeneous and isotropic Friedmann-Robertson-Walker (FRW) brane model and the evolution equations are reduced to an autonomous system by suitable transformation of variables. The nature of critical points are analyzed by evaluating the eigenvalues of linearized Jacobi matrix. Finally, the classical stability of the model is also studied.