Under a change of conditions, spiral waves in oscillatory reaction-diffusion media can become unstable and give rise to a multitude of emergent patterns. For example, in bounded domains spiral waves can undergo a resonant Hopf bifurcation leading to period-2 spirals which emit wave trains with doubled wavelength and temporal period and have a characteristic synchronization defect line. Here, we analyze the emergent patterns due to nonresonant Hopf bifurcations in the local dynamics giving rise to quasiperiodicity as reported in systems such as the peroxidase-oxidase and the Belousov-Zhabotinsky reaction. For a conceptual model of the peroxidase-oxidase reaction in a spatially extended medium, we find numerically that the additional frequency leads to defect-mediated turbulence. This proves that defect-mediated turbulence can indeed exist in media where the underlying local dynamics is quasiperiodic. While many statistical features of this turbulent dynamics are similar to those observed for other systems, we show that there are clear differences if higher-order statistics are considered. In particular, we find that the space-time dynamics of the topological defects as characterized by the statistics of defect loops is closely related to the underlying local dynamics.
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