Abstract
Recently the role of nonlinear oscillation in nature has been recognized not only in physical systems but also in biological systems. Among them, the synchronization and its breakdown are one of origins of the diversity of structures and complex behaviors in nature. The synchronization of two periodic oscillators are nowadays known as the Huygens phenomenon. When the synchronization of chaotic oscillators breaks down, an intermittency called the on-off intermittency is observed. In the present report, a simple interpretation on the onset of mechanism of on-off intermittency is briefly discussed by giving several concrete models exhibiting on-off intermittency. The intermittency is characterized by several characteristic statistics. It is shown that they can be derived by introducing a multiplicative stochastic process by rigorously solving the Fokker-Planck equation. Furthermore, results based on a solvable model of on-off intermittency recently proposed are compared with those of the stochastic model and other dynamical models.
