  We study the interactions between two atomic species in a binary
Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory
dynamics between the species, steady state solutions and their stability. By
employing a variational approach for a quasi one-dimensional, two-atomic
species, condensate we obtain equations of motion for the parameters of each
species: amplitude, width, position and phase. A further simplification leads
to a reduction of the dynamics into a simple classical Newtonian system where
components oscillate in an effective potential with a frequency that depends on
the harmonic trap strength and the interspecies coupling parameter. We develop
explicit conditions for miscibility that can be interpreted as a phase diagram
that depends on the harmonic trap's strength and the interspecies species
coupling parameter. We numerically illustrate the bifurcation scenario whereby
non-topological, phase-separated states of increasing complexity emerge out of
a symmetric state, as the interspecies coupling is increased. The
symmetry-breaking dynamical evolution of some of these states is numerically
monitored and the associated asymmetric states are also explored.
