We report the peculiar organization of oscillations in the forced Brusselator system, found in the parameter space as a nested structure of regular and chaotic phases. To this end, we apply the winding number concept, conceived for nonlinear driven oscillators, to expose all oscillatory phases in the nested structure. First, we use the period and torsion of orbits to describe every periodic oscillation in the parameter spaces, describing the nested structure in high-resolution phase diagrams. Next, we propose a basic structure organizing the periodicity, a “skeletal set” whose properties elucidate the genealogy and composition of oscillations in the nested structure. Finally, we discuss the application of the skeletal structure in a diversity of Brusselator’s oscillatory regimes.
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