Symmetry between laminar and burst phases for on-off intermittency

It is demonstrated both analytically and numerically that a symmetry exists between laminar and burst phases of on-off intermittency. The symmetry is a specific feature of on-off intermittency. It does not exist for the other types of regular Pomeau-Manneville and crisis-induced intermittency. A diffusional model, which incorporates reflecting barriers representing noise and nonlinearity, predicts the same scaling for the laminar and the burst lengths near the blowout bifurcation point. The symmetry of the scaling properties is demonstrated numerically for two systems exhibiting on-off intermittency, namely, the discrete three-dimensional Henon map and the unidirectionally coupled Rossler oscillators.