Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling

In a joint experimental and modeling approach we demonstrate chaos synchronization imposed by a delayed shared feedback coupling between two nonlinear electro-optic oscillators. Robust identical synchronization is obtained for both symmetric and strongly asymmetric timing of the mutual coupling, offering great potential for applications such as chaos-based communications. We further demonstrate antisynchronization as well as generalized synchronization with vanishing linear correlation, by detuning the nonlinearity in one of the oscillators.

Figure 1

Experimental setup of the electro-optic oscillators with delayed shared feedback coupling (DSFC).

Figure 2

(Color online) Cross-correlation functions from experiments (a) and numerics (c) and the corresponding time series in (b) and (d), $x_1\left(t\right)$ (black) and $x_2(t-\mathrm{\Delta }{t}_0)$ (red).

Figure 3

Cross-correlation properties for strongly asymmetric delays $T_1\ll T_2$: (a) experiment, (b) modeling.

Figure 4

(Color online) Perturbation signal (lower, gray), synchronization error $\left[x_1\right(t)-x_2(t-\mathrm{\Delta }{T}_0\left)\right]$ (lower, black), and time-resolved cross correlation (upper, red line), with $T_1\ll T_2$ as in Fig. 3.

Figure 5

Experimental cross correlation for $T_1\approx T_2$, but $\mathrm{\Delta }\Phi \ne 0$: (a) $\mathrm{\Delta }\Phi =\pi ∕2$ and (c) $\mathrm{\Delta }\Phi =\pi ∕4$. Corresponding modeling results are in (b) and (d). The inset in (d) is a circular synchronization plot.