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.