  We investigate the evolution of a flat Emergent Universe obtained with a
non-linear equation of state (nEoS) in Einstein's general theory of Relativity.
The nEoS is equivalent to three different types of barotropic cosmic fluids,
which are found from the nEoS parameter. The EU began expanding initially with
no interaction among the cosmic fluids. Assuming an interaction that sets in at
a time $t \geq t_i$ in the fluid components, we study the evolution of the EU
that leads to the present observed universe. We adopt a dynamical system
analysis method to obtain the critical points of the autonomous system for
studying the evolution of an EU with or without interaction in fluid
components. We also study the stability of critical points and draw the phase
portraits. The density parameters and the corresponding cosmological parameters
are obtained for both the non-interacting and interacting phases of the
evolution dynamics.
