We study experimentally chaos synchronization of nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. Coupling three oscillators in a chain, we find that the outer two oscillators always synchronize. In contrast, isochronal synchronization of the mediating middle oscillator is found only when self-feedback is added to the middle oscillator. We show how the stability of the isochronal solution of any network, including the case of three coupled oscillators, can be determined by measuring the synchronization threshold of two unidirectionally coupled systems. In addition, we provide a sufficient condition that guarantees global asymptotic stability of the synchronized solution.

We study the effect of asymmetric coupling strengths on the onset of oscillations in delay-coupled nonlinear systems. Our experiment consists of two wide-band optoelectronic devices that are cross-coupled. We find that oscillations appear in the system when the product of the two coupling strengths exceeds a critical value. Beyond the oscillation threshold, the oscillation amplitudes grow smoothly and we find a scaling law that describes the dependence of the amplitude on the coupling strengths. The observations are in good agreement with predictions from linear stability analysis and normal form theory.