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We carry out the dynamical system analysis of interacting dark energy-matterscenarios by examining the critical points and stability for not just thebackground level cosmological evolution, but at the level of the linear densityperturbations as well. While an analysis at the background level can lead to astable phase space trajectory implying that the universe eventually transpiresto a dark energy dominated (de-Sitter) era, a two-fold degeneracy in thespectrum of the critical points is found to arise in the inhomogeneous picture,due to the possible growth and decay of matter density perturbations. Analyzingthe phase space dynamics of the growth factor, we show that it turns out to begreater than unity initially, for one of the critical points, and leads to astable configuration as the fluctuations in the matter density die outasymptotically. As to the growth index, we show that the only trajectory whichis physically plausible is the one that evolves mildly at high redshifts andgets steeper as time progresses. However, such a trajectory amounts to theaverage value of the growth index, throughout the expansion history of theuniverse, not much deviated from the value $6/11$, corresponding to thebackground $\L$CDM cosmology.

Dynamical system analysis of interacting dark energy-matter scenarios at the linearized inhomogeneous level