Complex and transitive synchronization in a frustrated system of calling frogs

This letter reports synchronization phenomena and mathematical modeling on a frustrated system of living beings, or Japanese tree frogs (Hyla japonica). While an isolated male Japanese tree frog calls nearly periodically, he can hear sounds including calls of other males. Therefore, the spontaneous calling behavior of interacting males can be understood as a system of coupled oscillators. We construct a simple but biologically reasonable model based on the experimental results of two frogs, extend the model to a system of three frogs, and theoretically predict the occurrence of rich synchronization phenomena, such as triphase synchronization and 1:2 antiphase synchronization. In addition, we experimentally verify the theoretical prediction by ethological experiments on the calling behavior of three frogs and time series analysis on recorded sound data. Note that the calling behavior of three male Japanese tree frogs is frustrated because almost perfect antiphase synchronization is robustly observed in a system of two male frogs. Thus, nonlinear dynamics of the three-frogs system should be far from trivial.