From annular to interval dynamics: Symbolic analysis of the periodically forced Brusselator

In this paper we show that numerical study under the guidance of symbolic dynamics may provide an effective method to gain global knowledge on ODEs, which is difficult to obtain either by purely analytical or by completely numerical means. We demonstrate how this approach works in practice on the example of the periodically forced Brusselator. In particular, the transition from annular type dynamics to interval dynamics is explored in terms of symbolic dynamics. Our results are instructive for the study of other nonlinear systems with competing frequencies, as the method is topological in nature, but complemented with numerical details.