  We model the neuronal circuit of the C.elegans soil worm in terms of
Hindmarsh-Rose systems of ordinary differential equations, dividing its circuit
into six communities pointed out by the walktrap and Louvain methods. Using the
numerical solution of these equations, we analyze important measures of
dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and
the $\Phi_{\mbox{AR}}$ auto-regressive integrated information theory measure,
which has been suggested to reflect different levels of consciousness. We show
that $\Phi_{\mbox{AR}}$ provides a useful measure of the information contained
in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans
brain dynamic network generates more information than the sum of its
constituent parts, and that attains higher levels of integrated information for
couplings for which either all its communities are highly synchronized, or
there is a mixed state of highly synchronized and desynchronized communities.
Both situations are characterized by relatively low chaotic behavior.
