Dynamical system analysis of interacting dark energy in LRS Bianchi type I cosmology

This paper deals with an interacting dark energy (DE) model in Locally rotationally symmetric (LRS) Bianchi type I cosmological model with scalar field in the form of an exponential potential. We reduce the transformation equations to an independent system of ordinary differential equations by appropriate alteration of the variables to setup the complementary dynamical system and after that we also calculate the critical points of the system. We get six critical points when our coupling parameter is positive. And we get two critical points when our coupling parameter is negative. And dark energy behaves like a perfect fluid for all the critical points. And after that we analyzed all the critical points by calculating the eigenvalues of the Jacobian matrix and we find out that out of these eight critical points, six critical points are stable, which shows that our Universe is accelerating. And two (2) critical points are unstable. We also present the phase plot analysis.