Robust and ubiquitous on-off intermittency in active coupling

On-off intermittency is an aperiodic switching between synchronized dynamics and non-synchronized, chaotic, dynamics. Intermittency is observed near the onset of chaos on a bifurcation diagram produced by varying the parameters of its coupling strength. Therefore, its occurrence depends upon tuning the parameters of the system in a very sensitive way. In the present paper, a concept of observational heterarchy is reviewed with a simple model, and characters of on-off intermittency derived from active coupling systems (ACS) are investigated. Generally, on-off intermittency results from fluctuation of the local transverse Lyapunov exponent through points of marginal stability. ACS can retain such a character of the Lyapunov exponent by the time evolution of the maps, so on-off intermittency occurs on wider parameter regions. This paper presents a certain approach to the notion of robustness that is regarded as a persistent feature, conceptually different from the strict notion of stability on dynamical systems.