The origin of localized patterns with a spatiotemporal oscillatory background state.

The localized patterns observed with a spatiotemporal oscillatory background in the experiment are believed to emerge due to the bistability of supercritical Turing-Hopf modes. However, the branching origin of these patterns remains unclear. In this paper, we explore the formation of local patterns near the subcritical Turing-Hopf bifurcation point using the Gray-Scott model as an example.