  Variational algorithms have gained prominence over the past two decades as a
scalable computational environment for Bayesian inference. In this article, we
explore tools from the dynamical systems literature to study convergence of
coordinate ascent algorithms for mean field variational inference. Focusing on
the Ising model defined on two nodes, we fully characterize the dynamics of the
sequential coordinate ascent algorithm and its parallel version. We observe
that in the regime where the objective function is convex, both the algorithms
are stable and exhibit convergence to the unique fixed point. Our analyses
reveal interesting {\em discordances} between these two versions of the
algorithm in the region when the objective function is non-convex. In fact, the
parallel version exhibits a periodic oscillatory behavior which is absent in
the sequential version. Drawing intuition from the Markov chain Monte Carlo
literature, we {\em empirically} show that a parameter expansion of the Ising
model, popularly called as the Edward--Sokal coupling, leads to an enlargement
of the regime of convergence to the global optima.
