Bifurcation Structures of Period-Adding Phenomena in an Ocean Internal Wave Model

In this paper, we study bifurcation structures of period-adding phenomena in an internal wave model that is a mathematical model for ocean internal waves. It has been suggested that chaotic solutions observed in the internal wave model may be related to the universal property of the energy spectra of ocean internal waves. In numerical bifurcation analyses of the internal wave model, we illustrate bifurcation routes to chaos and parameter regions where chaotic behavior is observed. Furthermore, it is found that the chaotic solutions are related to the period-adding sequence, that is, successive generations of periodic solutions with longer periods as a control parameter is changed. Considering the period-adding sequence as successive local bifurcations, we discuss a mechanism of the phenomena from the viewpoint of bifurcation analysis. We also consider similarity between period-adding phenomena in the internal wave model and ones in the Lorenz model.