Dynamics of a Three-Coupled System in the Belousov-Zhabotinsky Reaction

The behavior of a three-coupled system of a one-dimensional return map of the Belousov-Zhabotinsky (BZ) reaction was studied, where the system was arranged in triangular form. This examination indicated that five types of synchronized modes appeared depending on the coupling strength. In this case, the one-dimensional return map of the BZ reaction was synchronized with the change from chaos to periodic oscillation. We also found that the rotation mode was dominant in the synchronized modes. On the other hand, in the logistic map, three types of synchronized modes appeared depending on the coupling strength, where the rotation mode was also observed. However, the region of the rotation mode was very small. On the basis of the present results, we also suggested that frustration played an important role in the three-coupled system arranged in triangular form.