Uncertainty in Chaos Synchronization

In this paper a variety of uncertainty phenomena in chaos synchronization, which are caused by the sensitive dependence on initial conditions and coupling strength, are numerically investigated. Two identical Chua’s circuits are considered for both mutuallyand unidirectionallycoupled systems. It is found that initial states of the system play an important role in chaos synchronization. Depending on initial conditions, distinct behaviors, such as in-phase synchronization, anti-phase synchronization, oscillation-quenching, and bubbling of attractors, may occur. Based on the findings, we clarify that the systems, which satisfy the standard synchronization criterion, do not necessarily operate in a synchronization regime.