Connecting chaotic regions in the Coupled Brusselator System

A family of vector fields describing two Brusselators linearly coupled by diffusion is considered. This model is a well-known example of how identical oscillatory systems can be coupled with a simple mechanism to create chaotic behavior. In this paper we discuss the relevance and possible relation of two chaotic regions. One of them is located using numerical techniques. The another one was first predicted by theoretical results and later studied via numerical and continuation techniques. As a conclusion, under the constrains of our exploration, both regions are not connected and, moreover, the former one has a big size, whereas the later one is quite small and hence, it might not be detected without the support of theoretical results. Our analysis includes a detailed analysis of singularities and local bifurcations that permits to provide a global parametric study of the system.