Strong acoustic interactions via a cross-talk section were investigated in two coupled model gas turbine combustors. In particular, we focused on the dynamical state of different acoustic interaction modes using several time series analysis methods, including phase portraits, Poincare maps, correlation dimensions, and histograms. Our results demonstrate that a period-1 limit cycle occurs for a push-push mode. By contrast, when a push-pull mode is excited in the system, a period-3 attractor emerges in the cross-talk section.