  In this work we consider a four compartment Brusselator system. The reaction
terms of this system are of non constant sign, thus components of the solution
are not bounded apriori, and functional means to derive apriori bounds will
fail. We prove global existence of solutions, via construction of an
appropriate lyapunov functional. Furthermore due to the sign changing
nonlinearities, the asymptotic sign condition is also not satisfied, causing
further difficulties in proving the existence of global attractor. These
difficulties are circumvented via the use of the lyapunov functional
constructed along with the use of the uniform gronwall lemma. We are able to
prove the existence of an attractor for the system, improving previous results
in the literature.The Hausdorff and fractal dimensions of the attractor are
also shown to be finite.In particular we derive a lower bound on the Hausdorff
dimension of the global attractor. We use numerical simulations,as well as
numerical attractor reconstruction methods via nonlinear time series analysis,
to validate our results.
