The sub-Lyapunov exponent of chaotic delay systems

The sub-Lyapunov exponent (sub-LE) has been introduced in the context of a drive-response scheme. It characterizes the conditional stability of the driven system and is therefore related to generalized synchronization. The concept can be extended to a system subject to an arbitrary drive. In this talk, we focus on the sub-LE of a delay system, where a nonlinear dynamical node is driven by its own time-delayed feedback, which often results in high-dimensional chaotic dynamics. The relationship of the sub-LE with correlation coefficients from time series of a single system or from a synchronization scheme of two systems will be shown. A method to extract the sub-LE directly from time series is introduced. Further, the sub-LE is measured in a consistency experiment with a semiconductor laser subject to two switching delay loops. As an outlook, the role of the fluctuations in the finite-time sub-LE will be discussed.