Self-oscillating chemical reactions are dynamical reaction-diffusion systems that show immense potential in the design of synthetic soft materials with biomimetic functionalities. The Belousov-Zhabotinsky (BZ) reaction is one such reaction, where the periodic change in the redox state of the metal ion catalyst drives the rhythmic chemical oscillations. Inspired by the exceptional properties of graphene, specifically its catalytic activity for redox reactions, we investigate the effect of graphene-based nanocomposites on the dynamics of the BZ reaction. In particular, we synthesized catalytic mats by decorating ceria nanoparticles (CeNPs) on graphene-based nanosheets, thereby creating 0D-2D heterostructures and subsequently, incorporate these catalytic mats into the BZ reaction. Our investigations reveal that CeNP decorated nanocomposites significantly enhance the oscillating frequency of the BZ reaction, not only compared to the traditional solution-based catalysts but also compared to the bare graphene-based nanosheets. From our experiments at various temperatures and concentrations, together with modelling and simulations, we determine the apparent rate constant for different CeNP decorated graphene nanocomposites. Ultimately, we determine the apparent rate and estimate various kinetic parameters, including activation energy and reaction order. In short, we demonstrate that CeNP decorated nanomats are excellent catalysts and elucidate that the kinetics of the BZ reaction can be simulated using the Oregonator model with our kinetic parameters. We envisage that our findings can be utilized to harness multiscale interactions to design a variety of multifunctional stimuli responsive materials.